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Ehlers

RS ve Beta Single by TeknikPiyasaThis indicator takes the real-time data provided by the "Technical Market: RS & Beta Strategy Matrix" one step further by visualizing the historical performance of a selected asset against the market. While the Matrix tells you "what it is right now," this analyzer shows you "how it got to this point" and the direction of the trend. 🔍 What Does It Do? While traditional indicators focus solely on the price movement of an asset, this tool analyzes the asset's strength and sensitivity relative to the overall market (benchmark). A stock's price may be rising, but if this rise lags behind the index, this indicator warns you and helps you move your capital to a more efficient area. 🎨 Visual Color Codes and Their Meanings The main line you see on the chart changes color in real-time based on the stock's strategic character: 🟢 AGGRESSIVE LEADER (Bright Green): The stock is both strong against the index and highly responsive to market enthusiasm. It is the main engine of rising trends. 🔵 CALM POWER (Blue): The stock manages to beat the index while doing so with lower volatility and stress. This is the ideal "safe haven" zone for medium-to-long-term investors. 🟠 RISKY FOLLOWER (Orange): The stock is weak relative to the index but highly sensitive to market fluctuations. This typically represents the risky zone, often referred to as a "falling knife." 🔴 WEAK / SLUGGISH (Red): This is the stagnant zone where both relative strength and market sensitivity are low, and capital inflow has stopped. 🚦 Signals and Timing The indicator not only determines the profile but also offers two critical visual tools for trade timing: RS Average (Navy Blue Line): The colored main line crossing above this navy blue average is an early signal that the stock is launching an attack against the index. Automatic Detection: Whichever stock you open on the chart, the indicator automatically pulls that data, leaving you only to choose the benchmark (BIST 100, USD/TRY, etc.) you wish to compare it against. 💡 Application Advice Main Trend: Waiting for the color on daily charts to turn from red to blue or green helps you find the "right stock." Timing: Once the stock is selected, switching to hourly charts and capturing the moments when the RS line rises above its own average provides the "right timing." "Relative strength tells you where the money is flowing; Beta whispers how turbulent that flow is." www.teknikpiyasa.com.tr
Indicador Pine Script®
por teknik_piyasa
Ehlers Super Smoother Trend Score [BackQuant]Ehlers Super Smoother Trend Score Overview Ehlers Super Smoother Trend Score is a regime and trend-strength indicator built on a signal-processing filter created by John F. Ehlers. Instead of smoothing price with a standard moving average (which is mathematically crude and prone to noise and aliasing), this indicator applies the Ehlers Super Smoother, a Butterworth-style low-pass filter designed specifically for market data. The filtered series is then scored for directional persistence across a configurable lookback window, producing an oscillator-like trend score that measures how consistently the smoothed trend is advancing or deteriorating. This is not a simple “MA slope” tool. It is: A proper low-pass filter (Super Smoother) to reduce noise while preserving structure. A persistence score that converts the filtered trend into a quantitative regime signal. A threshold framework that turns the score into long/short regime transitions with clean state logic. Where the filter comes from (and why it matters) John F. Ehlers is known for applying digital signal processing (DSP) techniques to technical analysis. Traditional moving averages are not designed as proper frequency-selective filters. They blur price, lag heavily, and can introduce distortions, especially when the market contains high-frequency components (noise) near the Nyquist limit (the maximum representable frequency in sampled data). The Super Smoother is derived from a Butterworth low-pass filter design. Butterworth filters are engineered to have a maximally flat passband, meaning they smooth without introducing ripples in the filtered output. In trading terms: Less “wavy” smoothing artifacts than many MA variants. Better suppression of high-frequency noise. Cleaner trend structure for downstream logic. This script implements Ehlers’ recursive coefficient form, giving you a 2-pole (classic) or 3-pole (heavier) filter. What “Super Smoother” actually is The Super Smoother is a recursive IIR filter (Infinite Impulse Response). Unlike an SMA which averages a fixed window of past values, an IIR filter uses feedback from its own prior output values. That matters because it can achieve strong smoothing with less lag for a given “smoothness target.” Conceptually: Input: price series. Output: filtered estimate of the “low-frequency” component (trend structure). Mechanism: combine current input (or pre-filtered input) with previous filter outputs using coefficients derived from a chosen cutoff period. The coefficients (c1–c4) are not arbitrary, they are computed from exponential decay and cosine terms based on the cutoff period. This is what makes it a real DSP filter rather than “just another MA.” 2-pole vs 3-pole behavior 2-pole (classic) A standard Ehlers Super Smoother configuration. It offers a strong improvement over typical MAs in smoothness vs lag balance. 3-pole Adds an additional feedback term (one more prior filtered state). This increases smoothing and noise rejection, but introduces slightly more lag. The advantage is a cleaner structural line, which often improves regime stability when the market is noisy or mean-reverting. Anti-aliasing pre-filter step Before applying the recursive formula, the script averages the current and previous price: avg = (src + src ) / 2 This is a simple but important pre-filter that reduces high-frequency components that can alias into lower frequencies in sampled data. In practice, it helps stop “one-bar spikes” from contaminating the filter output as much. Inputs and what they really control Super Smoother Period (ssPeriod) This is the cutoff period used in the coefficient derivation. It is not the same as “MA length,” but it behaves similarly in that: Lower period = faster response, less smoothing, more sensitivity to noise. Higher period = smoother output, better noise rejection, more lag. Poles Selects filter order: 2 poles = balanced default. 3 poles = smoother, more conservative. Score Lookback Start/End Defines the persistence scoring window. The script compares the current filtered value to many prior filtered values across that range. A longer range makes the score more “confidence-based” and slower to change, while a shorter range makes it more reactive. Thresholds (Long/Short) Turns the score into a regime classification: Long threshold defines when bullish persistence is strong enough to be considered a trend regime. Short threshold defines when persistence has deteriorated enough to signal a bearish transition. How the trend score is computed After filtering, the indicator computes a directional persistence score on the filtered series (not raw price). That distinction matters because you are scoring structure, not noise. Mechanically: For each i in the scoring window: - If filt_now > filt , add +1 - Else add -1 Sum across the window to produce the score. Interpretation: High positive score means the filtered trend is consistently higher than many past points, persistent bullish structure. Low or negative score means the filtered trend is not advancing, or is consistently below prior points, bearish structure. Scores near the middle mean the filtered series is oscillating without clear persistence, chop or transition. This is a persistence metric, not a slope metric. It does not care about one-bar direction, it cares about consistency relative to history. Signal and state logic (why it stays clean) The indicator uses state logic to prevent constant flip-flopping: Long condition: score > long threshold. Short condition: score crosses below short threshold (uses prevScore and current score). That short logic is event-based, it triggers only on the breakdown transition, not on every bar below the threshold. Once a regime is set, it remains until a real threshold event forces change. Signals are plotted only on regime flips: Long marker when signal becomes +1 and prior was -1. Short marker when signal becomes -1 and prior was +1. This is designed for alerts and for clean backtesting interpretation. Visual layers The indicator can be used purely as a panel oscillator or as a structure overlay. Pane Trend Score line, colored by active regime. Optional reference lines at long/short thresholds for fast regime reading. On-chart (optional) Super Smoother line plotted over price, colored by regime. Optional candle painting and background shading to reflect active regime. This lets you treat the filter as a dynamic trend structure line while using the score as the regime classifier. How to interpret it properly 1) The Super Smoother line This is the cleaned trend structure estimate: When price respects the smoother line, trend structure is intact. When price repeatedly chops through it, structure is weak or range-bound. 2) The score This is the quantified persistence of that structure: Rising score implies strengthening trend persistence. Falling score implies deterioration, transition risk, or mean reversion. Score compression often shows consolidation before a regime shift. 3) Threshold regimes Above long threshold: bullish persistence regime, trend-following conditions. Below short threshold: bearish regime transition, defensive or short-biased conditions. Between thresholds: neutral/transition zone, where chop and fakeouts are common. Practical use cases Trend filter Only take long setups when score is above the long threshold. Reduce exposure or avoid trend trades in the neutral band. Treat a breakdown through the short threshold as regime invalidation. Trend quality assessment High score = continuation environment. Moderate score = trend exists but is fragile. Low/negative score = distribution, downtrend, or unstable structure. Trade management Use the Super Smoother line as a structure reference for trailing risk. Use score deterioration as an early warning before full regime flips. Use regime flips as hard exits or bias changes. Tuning guidelines If you want fewer signals and cleaner regimes Increase ssPeriod. Use 3 poles. Increase scoreEnd (longer scoring window). If you want faster reaction Decrease ssPeriod. Use 2 poles. Reduce the scoring window length. Keep in mind: faster settings increase sensitivity to chop. The filter is good, but no filter removes the reality of mean reversion. What makes this different from “just a smoothed MA score” The difference is the filter quality. The Super Smoother is a proper low-pass filter with coefficients derived from DSP principles, designed to suppress high-frequency noise and avoid common smoothing artifacts. Scoring that filtered structure gives you a regime metric that is more stable and more meaningful than scoring raw price or scoring a basic MA that still carries a lot of aliasing and distortion. Summary Ehlers Super Smoother Trend Score combines a DSP-derived Butterworth-style Super Smoother filter with a directional persistence scoring model. The filter provides a clean, low-noise trend structure series, and the score quantifies how consistently that structure is advancing or deteriorating across a defined window. Threshold-based regime logic converts the score into clean trend states and alerts, making it a practical tool for trend filtering, regime detection, and structure-aware trade management.
Indicador Pine Script®
por BackQuant
4
Ehlers Adaptive Trend FilterEHLERS ADAPTIVE TREND FILTER | Lag-Compensated SuperSmoother Based on John Ehlers' "Smoothing The Data" (2014), this indicator extends the SuperSmoother with hybrid Butterworth filters and dynamic lag compensation. ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ KEY FEATURES: ✓ 3 FILTER MODES (lag-measured empirically) • 2p+2p (Fast): 62 bars lag — responsive, great for scalping • 3p+2p (Hybrid): 70 bars lag — RECOMMENDED, best risk/reward • 3p+3p (Smooth): 88 bars lag — ultra-smooth for macro trends ✓ LAG-COMPENSATED MOMENTUM Automatically extends momentum lookback to account for filter delay. Keeps momentum signals responsive despite heavy smoothing. ✓ CONFIRMATION-BASED REVERSALS Requires 2+ bars confirmation before signaling reversals. ~60% fewer false signals than single-bar detection. Reduces whipsaws on volatile assets. ✓ VOLATILITY-ADAPTIVE THRESHOLDS Automatically scales all deviation levels based on asset volatility. Works seamlessly across: - Crypto (20%+ volatility) - Equities (10-15% volatility) - Forex (2-5% volatility) - Bonds (<2% volatility) ✓ MULTI-TIMEFRAME AUTO-CALIBRATION Automatically optimizes filter periods for your trading style: - Scalping (<1H): 2p+2p (Fast) - Swing Trading (1D): 3p+2p (Hybrid) ← Default - Position Trading (1W+): 3p+3p (Smooth) ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ WHAT YOU GET IN THE DASHBOARD: • TREND STATUS: Good/Bad (signal above/below baseline) • MOMENTUM: Strong/Steady/Weak/Opposing (lag-compensated) • MOMENTUM TREND: Increasing/Decreasing/Stable • SUPPORT BASELINE: Bull Reversal/Bear Reversal/Aligned • SUPPORT SLOPE: Positive/Negative/Neutral (with %) • SAFETY MARGIN: % distance from baseline • PRICE DEVIATION: Extended/Expanding/On Course/Lagging • TECHNICAL RATING: Perfect/Transition/Dangerous/Critical • VOLATILITY: Live % + historical baseline • FILTER CONFIG: Active mode + exact lag metric • THRESHOLD LEVELS: Adaptive or Fixed mode • ANALYSIS MODE: Auto-calibrated or Manual ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ PERFORMANCE (Backtested 2020-2024): ES 1D (3p+2p Hybrid): ✓ 68% Win Rate | 2.2:1 Profit Factor ✓ 12% Max Drawdown | Avg Trade: +45 points BTC 4H (3p+2p Hybrid): ✓ 62% Win Rate | 1.9:1 Profit Factor ✓ 18% Max Drawdown | Avg Trade: +$280 EURUSD 1H (2p+2p Fast): ✓ 55% Win Rate | 1.7:1 Profit Factor ✓ 8% Max Drawdown | Avg Trade: +45 pips ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ HOW TO USE: 1. Add indicator to chart (any asset, any timeframe) 2. Select Filter Configuration: → 3p+2p (Hybrid) recommended for most traders 3. Read the dashboard (bottom-right table) 4. Trade signals: → ENTER: Trend Status = "Good" + Momentum = "Strong" → EXIT: Trend Status = "Bad" OR background highlight appears 5. Combine with your own trade plan (entries, sizing, risk management) ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ WHY THIS INDICATOR? Most traders face a painful choice: → Fast MA (like EMA20): Responsive but too many false signals → Slow MA (like EMA100): Smooth but miss 20% of moves Ehlers SuperSmoother solves this using 40+ years of digital signal processing research. Butterworth filters preserve trend direction while removing high-frequency noise more efficiently than moving averages. The innovation: LAG COMPENSATION By measuring the exact delay of each filter and dynamically adjusting momentum lookback windows, you get BOTH clean trends AND responsive signals. ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ TECHNICAL DETAILS: Filter Type: Ehlers 2-Pole & 3-Pole SuperSmoother (Butterworth) Lag Compensation: Empirically measured via step response Momentum Adjustment: 1.0x (2p+2p) / 1.15x (3p+2p) / 1.45x (3p+3p) Volatility Model: 75th percentile of rolling 252-day returns Reversal Confirmation: 2-bar minimum (reduces noise) Repainting: NO (Pine Script v6, confirmed bars only) ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ DISCLAIMER: This indicator is for educational and analytical purposes only. NOT financial advice, investment recommendations, or profit guarantees. • Past performance does NOT guarantee future results • All trading involves risk, including loss of principal • Test extensively on historical data before live trading • "Safety" and "Risk" metrics measure technical deviation, NOT capital protection • Start with small position sizes and proper risk management ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ REFERENCE: Ehlers, J. (2014). "Smoothing The Data." Stocks & Commodities Magazine. Oppenheim & Schafer. "Discrete-Time Signal Processing" (3rd ed.)
Indicador Pine Script®
por TrendMatrix_Labs
TASC 2026.01 The Reversion Index█ OVERVIEW This script implements the Reversion Index as presented by John F. Ehlers in the January 2026 edition of the TASC Traders' Tips , "Identifying Peaks And Valleys In Ranging Markets”. This indicator was created to provide timely buy and sell signals for mean reversion strategies. █ CONCEPTS Ehlers came up with the idea for the Reversion Index following the development of the "Continuation Index" (featured in the September 2025 edition). While the Continuation Index provides indications for trend onset, continuation, and exhaustion; the Reversion Index serves as its counterpart for mean-reversion trading. The raw Reversion Index value is calculated as the net change in price normalized to the sum of the absolute value of change in price over the same period; for clarity, it is then smoothed using Ehlers' SuperSmoother. The Smooth Reversion Index value is led by a "Trigger" line, which is created by smoothing the raw data to half the smoothing period of the smoothed index. Note: Ehlers suggests the smoothing lengths be left at 8 and 4 (Reversion Index & Trigger). For this reason these lengths are hard-coded in the script but can be easily modified in the code. █ USAGE In order to identify peaks and valleys effectively, the "Length" should ideally be set to half of that of the expected cycle of the data. If the expected cycle of your trading data is 20 bars, a 10 bar length should be set. Note: The Reversion Index is intended to identify peaks and valleys within a cycle, not over a large sample period. Ehlers suggests that this would create an estimation of trend, which is not the goal here. Once the length is set, peaks and valleys are interpreted as the cross of the "Trigger" and "Smooth" lines.
Indicador Pine Script®
por PineCodersTASC
MAMA - FAMA (Ehlers) [KN]MAMA - FAMA (Ehlers) Surprisingly, I couldn't find a proper Pine Script implementation of this classic indicator on TradingView, so here's my version. This indicator implements John Ehlers' MESA Adaptive Moving Average (MAMA) and Following Adaptive Moving Average (FAMA) from his book "Rocket Science for Traders." How It Works Unlike traditional moving averages with fixed periods, MAMA adapts its smoothing based on the market's dominant cycle. It uses the Hilbert Transform to measure the instantaneous phase of price, then adjusts its responsiveness according to how fast that phase is changing. When price is trending strongly (rapid phase change), MAMA speeds up to follow closely. During consolidation (slow phase change), it slows down to filter noise. FAMA is a further smoothed version of MAMA that serves as a signal line. Signals 🔵 Bullish : MAMA crosses above FAMA 🟠 Bearish : MAMA crosses below FAMA The adaptive nature makes this particularly effective at avoiding whipsaws during ranging markets while still catching trends early. Inputs - Fast Limit (default 0.5): Maximum alpha, controls fastest response - Slow Limit (default 0.05): Minimum alpha, controls slowest response - Source (default hl2): Price input Credits Original concept by John F. Ehlers.
Indicador Pine Script®
por KatherinaNote
Ehlers Dominant Cycle Stochastic RSIEhlers Enhanced Cycle Stochastic RSI OVERVIEW The Ehlers Enhanced Cycle Stochastic RSI is a momentum oscillator that automatically adjusts its lookback periods based on the dominant market cycle. Unlike traditional Stochastic RSI which uses fixed periods, this indicator detects the current cycle length and scales its calculations—making it responsive in fast markets and stable in slow ones. The indicator combines John Ehlers' digital signal processing research with the classic Stochastic RSI indicator, then adds a confirmation system to ensure cycle measurements are reliable. THE THEORY Traditional oscillators use fixed lookback periods (ie, 14-bar RSI). This creates a fundamental problem: markets don't move in fixed cycles. A 14-period RSI might capture the rhythm perfectly during one market phase, then completely miss it when conditions change. Ehlers' research demonstrated that price data contains measurable cyclical components. If you can detect the dominant cycle length, you can tune your indicators to match it—like tuning a radio to the right frequency. This indicator takes that concept further by using three independent cycle detection methods and only trusting the measurement when they agree: Hilbert Transform — A mathematical technique from signal processing that extracts cycle period from the phase relationship between price and its derivative. It is fast but can be noisy. Autocorrelation Periodogram — Measures how similar the price series is to lagged versions of itself. The lag with highest correlation reveals the dominant cycle. More stable than Hilbert, but slightly slower to adapt. Goertzel Algorithm (DFT) — A frequency-domain approach that calculates spectral power at each candidate period. Identifies which frequencies contain the most energy. When all three methods converge on similar period estimates, confidence is high. When they disagree, the market may be in a non-cyclical or in transition. HOW IT CHANGES THE STOCHASTIC RSI Standard Stochastic RSI: 1. Calculate RSI with fixed period (14 bars) 2. Apply Stochastic formula over fixed period (14 bars) 3. Smooth with fixed periods Ehlers Enhanced Cycle Stochastic RSI: 1. Detect dominant cycle using three methods 2. Confirm cycle measurement (methods must agree) 3. Calculate RSI with period scaled to the detected cycle 4. Apply Stochastic formula with cycle-scaled lookback 5. Smooth adaptively The result: when the market is cycling quickly (say, 15-bar cycles), the indicator uses shorter periods and responds faster. When the market stretches into longer cycles (such as 40-bar cycles), it automatically extends its lookback to avoid whipsaws. The Period Multipliers let you fine-tune this relationship: • 1.0 = Use the full detected cycle (smoother, fewer signals) • 0.5 = Use half the cycle (more responsive, catches turns earlier) INTERPRETATION Reading the Oscillator: • K Line (Blue) — The main signal line. Moves between 0 and 100. • D Line (Orange) — Smoothed version of K. Use for confirmation. • Above 80 — Overbought. Momentum stretched to upside. • Below 20 — Oversold. Momentum stretched to downside. • Crossovers — K crossing above D suggests bullish momentum shift; K crossing below D suggests bearish. Spectral Dilation (optional): When enabled, applies a bandpass filter before cycle detection. This isolates the frequency band of interest and reduces noise. Useful for: • Very noisy instruments • Lower timeframes • When confidence stays persistently low
Indicador Pine Script®
por B3AR_Trades
Phase Coherence Index (PCI) — Hilbert Prototype v0.1Phase Coherence Index (PCI) — Hilbert Prototype v0.1 ✨ Concept: The Phase Coherence Index (PCI) measures the degree of phase alignment among multiple trend components derived from band-filtered price signals. In simpler terms, PCI quantifies how “in-sync” short, mid, and long-term market oscillations are. A high PCI (values near 100) means the market’s cyclical components are moving together — a state of phase alignment that typically accompanies sustained, directional trends. A low PCI (values near 0) indicates phase disorder or divergence between timeframes — often seen during transitions, chop, or volatility compression phases. ✨ How it works: 1. Multi-Band Extraction The price series is decomposed into three frequency bands using a simple EMA-difference bandpass filter: Short-term band Mid-term band Long-term band 2. Hilbert Quadrature Approximation For each band, a Hilbert-style quadrature signal (Q) is estimated using an Ehlers-inspired FIR kernel with coefficients h0=0.0962 and h1=0.5769. The original bandpass (I) and its quadrature (Q) form a complex phasor that carries instantaneous phase information. 3. Phase Extraction The arctangent of Q/I gives the phase angle (−π to π). Each band’s phase represents the “timing” of its oscillation relative to price movement. 4. Coherence Calculation All three band phases are converted to unit phasors (cos φ, sin φ). The average of these phasors is taken, and the magnitude of the resulting vector defines the PCI value: PCI = |mean_phasor| × 100 PCI = 100 → perfect phase alignment PCI = 0 → complete phase randomness 5. Smoothing and Regime Coloring The raw PCI is lightly smoothed by EMA to stabilize readings. A simple SuperTrend regime filter (ATR length 5, factor 6) colors the PCI line: Green: uptrend regime Red: downtrend regime Gray: low-coherence or neutral zone ✨ How to interpret PCI High PCI (≥70): Indicates strong phase coherence — multi-timeframe alignment, stable directional energy. Often coincides with trend persistence or mature momentum phases. Low PCI (≤30): Suggests phase dispersion or regime transition — signals are desynchronized across bands. Common near reversals, volatility compressions, or sideways congestion. Cross-phase Transitions: Rapid drops in PCI often precede periods of uncertainty or trend fatigue. Rising PCI after a contraction suggests emerging order or trend formation. ✨ Visualization PCI Line: Displays phase coherence magnitude (0–100). Color changes dynamically with SuperTrend regime. Dotted Reference Levels: 70 (high coherence), 30 (low coherence), 50 (midline). Optional Label: When PCI is high, a text label appears indicating whether the average phase bias leans bullish or bearish. ✨ Practical Use Combine PCI with momentum or volatility tools (e.g., RSI, ATR, DFI) to detect when multiple timeframes become synchronized. Use PCI drops (<30) as early warnings for possible trend exhaustion or market disorder. Use PCI rises (>70) as confirmation of trend continuation or emerging coherence. ✨ Limitations PCI measures phase alignment, not directional bias. It should be combined with a directional filter (e.g., SuperTrend, slope, or moving average). The Hilbert approximation is not a true analytic signal, but a real-time proxy optimized for stability. PCI is best interpreted as a structural context indicator rather than a direct entry signal. ✨ Educational intent This script is designed for quantitative study and visualization of phase alignment, not for direct trading advice. It demonstrates how Hilbert-style phasors and vector averaging can reveal coherence across timescales — a foundational concept for spectral, cyclical, and structural analysis. ✨ Disclaimer This script is provided for educational purposes only. It does not constitute financial advice. Trading involves risk; use at your own discretion. © 2025 Trading Playground Labs — “Phase Coherence Index (Hilbert Prototype v0.1) ─────────────────────────────── 📘 한국어 설명 (Korean translation below) ─────────────────────────────── Phase Coherence Index (PCI) — Hilbert Prototype v0.1 (한국어 설명) ✨ 개념 Phase Coherence Index (PCI) 는 여러 주기의 추세 구성 요소들 간에 위상의 정합 정도를 측정하는 지표입니다. 쉽게 말하면, 시장의 단기·중기·장기 진동(사이클)들이 서로 얼마나 “같은 박자”로 움직이는지를 수치화한 것입니다. PCI 값이 100에 가까울수록 시장의 주기적 구성 요소들이 함께 움직이고 있다는 뜻이며, 이는 일반적으로 지속적인 방향성 추세(trend persistence) 상태를 의미합니다. 반대로 PCI 값이 0에 가까울수록 각 주기의 움직임이 서로 엇박자 상태로 흐르며, 이는 전환기(chop), 혼돈(chaos), 혹은 압축(squeeze) 상태를 반영합니다. ✨ 작동 원리 1. 다중 밴드 추출 가격 데이터를 3개의 주파수 대역으로 분리합니다. 단기 (short-term band) 중기 (mid-term band) 장기 (long-term band) 각 대역은 빠른 EMA와 느린 EMA의 차이(EMA difference)로 얻은 단순한 밴드패스로 계산됩니다. 2. Hilbert 직교 성분 근사 각 밴드에 대해 Ehlers 계열 FIR 필터를 이용한 Hilbert 근사 신호(Q)를 계산합니다. 원본 밴드패스 신호(I)와 Q를 결합하면 복소 위상(phasor) 를 구성할 수 있고, 이를 통해 각 대역의 순간 위상(instantaneous phase) 을 추정합니다. 3. 위상 계산 Q/I의 아크탄젠트 값을 구하면 위상각 φ(−π ~ π)가 도출됩니다. 이 위상은 해당 주기의 진동 타이밍을 나타냅니다. 4. 위상 정합(Phase Coherence) 계산 각 밴드의 위상을 단위 페이저 벡터 (cos φ, sin φ)로 변환합니다. 세 벡터의 평균을 구하고, 그 평균 벡터의 크기를 0~100 스케일로 변환한 값이 PCI입니다. PCI = |평균 페이저| × 100 PCI = 100 → 완전한 위상 일치 PCI = 0 → 완전한 위상 무질서 5. 스무딩 및 추세 컬러링 계산된 PCI는 EMA로 약간 평활화되어 안정적으로 표시됩니다. 또한, SuperTrend 레짐 필터(ATR=5, Factor=6) 로 추세 방향에 따라 색이 바뀝니다: 초록색: 상승 추세 빨간색: 하락 추세 회색: 저정합 / 중립 구간 ✨ 해석 방법 PCI ≥ 70 (높은 정합) 여러 타임프레임이 같은 방향으로 동기화되어 있는 상태입니다. 이는 추세 지속성, 모멘텀 유지, 구조적 안정 상태를 의미합니다. PCI ≤ 30 (낮은 정합) 각 주기 간 위상 불일치가 심해지며, 시장이 방향을 잃거나 변곡점에 근접한 상황입니다. 보통 조정기, 변동성 축소, 횡보 국면에서 자주 나타납니다. 급격한 변동 (Phase Transition) PCI가 급격히 하락하는 구간은 추세 피로(trend fatigue) 또는 혼돈 국면 진입의 신호일 수 있으며, 이후 PCI가 상승하기 시작하면 새로운 질서(추세 형성) 가 시작될 가능성을 의미합니다. ✨ 시각화 구성 PCI 라인: 위상 정합도의 크기(0~100)를 표시합니다. SuperTrend 방향에 따라 색이 동적으로 변합니다. 점선 기준선: 70(높은 정합), 50(중간), 30(낮은 정합) 기준으로 시각화됩니다. 평균 위상 라벨: PCI가 높을 때, 평균 위상의 방향이 상승(bullish) 인지 하락(bearish) 인지를 라벨로 표시합니다. ✨ 활용 방법 RSI, ATR, DFI 등 다른 모멘텀/변동성 지표와 함께 사용하면, 복수 타임프레임 동기화 구간을 탐지할 수 있습니다. PCI 하락(30 이하)은 추세 피로 또는 혼돈 진입의 신호로, PCI 상승(70 이상)은 질서 회복 또는 추세 지속의 신호로 해석할 수 있습니다. 추세 전환, 조정, 또는 모멘텀 재편성 구간을 감지하는 데 유용합니다. ✨ 한계점 PCI는 방향성(Direction)을 직접 측정하지 않고, 구조적 정합(Alignment) 만 측정합니다. 따라서 반드시 방향 필터(SuperTrend, MA 기울기 등)와 함께 해석해야 합니다. Hilbert 근사는 완전한 복소 해석 신호가 아니라, 실시간 안정성을 중시한 근사 모델입니다. PCI는 진입 시그널용보다는 시장 구조 인식용 보조 지표로 적합합니다. ✨ 교육적 목적 이 스크립트는 위상 정합(phase coherence) 개념의 시각화와 정량적 연구를 위한 목적으로 설계되었습니다. 힐버트 변환 기반 위상 벡터(phasor) 와 벡터 평균화(vector averaging) 의 개념을 통해 시장의 다중 시간 구조 간 일관성(coherence)을 탐색할 수 있습니다. ✨면책 이 지표는 교육 목적으로만 제공됩니다. 투자 조언이 아니며, 모든 트레이딩 결정의 책임은 사용자에게 있습니다. © 2025 Trading Playground Labs — Phase Coherence Index (Hilbert Prototype v0.1) Developed for structural & spectral analysis of market phase alignment.
Indicador Pine Script®
por Cyan_TPM
MESA Adaptive Ehlers Flow | AlphaNattMESA Adaptive Ehlers Flow | AlphaNatt An advanced adaptive indicator based on John Ehlers' MESA (Maximum Entropy Spectrum Analysis) algorithm that automatically adjusts to market cycles in real-time, providing superior trend identification with minimal lag across all market conditions. 🎯 What Makes This Indicator Revolutionary? Unlike traditional moving averages with fixed parameters, this indicator uses Hilbert Transform mathematics to detect the dominant market cycle and adapts its responsiveness accordingly: Automatically detects market cycles using advanced signal processing MAMA (MESA Adaptive Moving Average) adapts from fast to slow based on cycle phase FAMA (Following Adaptive Moving Average) provides confirmation signals Dynamic volatility bands that expand and contract with cycle detection Zero manual optimization required - the indicator tunes itself 📊 Core Components 1. MESA Adaptive Moving Average (MAMA) The MAMA is the crown jewel of adaptive indicators. It uses the Hilbert Transform to measure the market's dominant cycle and adjusts its smoothing factor in real-time: During trending phases: Responds quickly to capture moves During choppy phases: Smooths heavily to filter noise Transition is automatic and seamless based on price action Parameters: Fast Limit: Maximum responsiveness (default: 0.5) - how fast the indicator can adapt Slow Limit: Minimum responsiveness (default: 0.05) - maximum smoothing during consolidation 2. Following Adaptive Moving Average (FAMA) The FAMA is a slower version of MAMA that follows the primary signal. The relationship between MAMA and FAMA provides powerful trend confirmation: MAMA > FAMA: Bullish trend in progress MAMA < FAMA: Bearish trend in progress Crossovers signal potential trend changes 3. Hilbert Transform Cycle Detection The indicator employs sophisticated DSP (Digital Signal Processing) techniques: Detects the dominant cycle period (1.5 to 50 bars) Measures phase relationships in the price data Calculates adaptive alpha values based on cycle dynamics Continuously updates as market character changes ⚡ Key Features Adaptive Alpha Calculation The indicator's "intelligence" comes from its adaptive alpha: Alpha dynamically adjusts between Fast Limit and Slow Limit based on the rate of phase change in the market cycle. Rapid phase changes trigger faster adaptation, while stable cycles maintain smoother response. Dynamic Volatility Bands Unlike static bands, these adapt to both ATR volatility AND the current cycle state: Bands widen when the indicator detects fast adaptation (trending) Bands narrow during slow adaptation (consolidation) Band Multiplier controls overall width (default: 1.5) Provides context-aware support and resistance Intelligent Color Coding Cyan: Bullish regime (MAMA > FAMA and price > MAMA) Magenta: Bearish regime (MAMA < FAMA and price < MAMA) Gray: Neutral/transitional state 📈 Trading Strategies Trend Following Strategy The MESA indicator excels at identifying and riding strong trends while automatically reducing sensitivity during choppy periods. Entry Signals: Long: MAMA crosses above FAMA with price closing above MAMA Short: MAMA crosses below FAMA with price closing below MAMA Exit/Management: Exit longs when MAMA crosses below FAMA Exit shorts when MAMA crosses above FAMA Use dynamic bands as trailing stop references Mean Reversion Strategy When price extends beyond the dynamic bands during established trends, look for bounces back toward the MAMA line. Setup Conditions: Strong trend confirmed by MAMA/FAMA alignment Price touches or exceeds outer band Enter on first sign of reversal toward MAMA Target: Return to MAMA line or opposite band Cycle-Based Swing Trading The indicator's cycle detection makes it ideal for swing trading: Enter on MAMA/FAMA crossovers Hold through the detected cycle period Exit on counter-crossover or band extremes Works exceptionally well on 4H to Daily timeframes 🔬 Technical Background The Hilbert Transform The Hilbert Transform is a mathematical operation used in signal processing to extract instantaneous phase and frequency information from a signal. In trading applications: Separates trend from cycle components Identifies the dominant market cycle without curve-fitting Provides leading indicators of trend changes MESA Algorithm Components Smoothing: 4-bar weighted moving average for noise reduction Detrending: Removes linear price trend to isolate cycles InPhase & Quadrature: Orthogonal components for phase measurement Homodyne Discriminator: Calculates instantaneous period Adaptive Alpha: Converts period to smoothing factor MAMA/FAMA: Final adaptive moving averages ⚙️ Optimization Guide Fast Limit (0.1 - 0.9) Higher values (0.5-0.9): More responsive, better for volatile markets and lower timeframes Lower values (0.1-0.3): Smoother response, better for stable markets and higher timeframes Default 0.5: Balanced for most applications Slow Limit (0.01 - 0.1) Higher values (0.05-0.1): Less smoothing during consolidation, more signals Lower values (0.01-0.03): Heavy smoothing during chop, fewer but cleaner signals Default 0.05: Good noise filtering while maintaining responsiveness Band Multiplier (0.5 - 3.0) Adjust based on instrument volatility Backtest to find optimal value for your specific market 1.5 works well for most forex and equity indices Consider higher values (2.0-2.5) for cryptocurrencies 🎨 Visual Interpretation The gradient visualization shows probability zones around the MESA line: MESA line: The adaptive trend center Band expansion: Indicates strong cycle detection and trending Band contraction: Indicates consolidation or ranging market Color intensity: Shows confidence in trend direction 💡 Best Practices Let it adapt: Give the indicator 50+ bars to properly calibrate to the market Combine timeframes: Use higher timeframe MESA for trend bias, lower for entries Respect the bands: Price rarely stays outside bands for extended periods Watch for compression: Narrow bands often precede explosive moves Volume confirmation: Combine with volume for higher probability setups 📊 Optimal Timeframes 15m - 1H: Day trading with Fast Limit 0.6-0.8 4H - Daily: Swing trading with Fast Limit 0.4-0.6 (recommended) Weekly: Position trading with Fast Limit 0.2-0.4 ⚠️ Important Considerations The indicator needs time to "learn" the market - avoid trading the first 50 bars after applying Extreme gap events can temporarily disrupt cycle calculations Works best in markets with detectable cyclical behavior Less effective during news events or extreme volatility spikes Consider the detected cycle period for position holding times 🔍 What Makes MESA Superior? Compared to traditional indicators: vs. Fixed MAs: Automatically adjusts to market conditions instead of using one-size-fits-all parameters vs. Other Adaptive MAs: Uses true DSP mathematics rather than simple volatility adjustments vs. Manual Optimization: Continuously re-optimizes itself in real-time vs. Lagging Indicators: Hilbert Transform provides earlier trend change detection 🎓 Understanding Adaptation The magic of MESA is that it solves the eternal dilemma of technical analysis: be fast and get whipsawed in chop, or be smooth and miss the early move. MESA does both by detecting when to be fast and when to be smooth. Adaptation in Action: Strong trend starts → MESA quickly detects phase change → Fast Limit kicks in → Early entry Trend continues → Phase stabilizes → MESA maintains moderate speed → Smooth ride Consolidation begins → Phase changes slow → Slow Limit engages → Whipsaw avoidance 🚀 Advanced Applications Multi-timeframe confluence: Use MESA on 3 timeframes for high-probability setups Divergence detection: Watch for MAMA/price divergences at band extremes Cycle period analysis: The internal period calculation can guide position duration Band squeeze trading: Narrow bands + MAMA/FAMA cross = high-probability breakout Created by AlphaNatt - Based on John Ehlers' MESA research. For educational purposes. Always practice proper risk management. Not financial advice. Always DYOR.
Indicador Pine Script®
por AlphaNatt
2
Cycle-Synced Channel Breakout📌 Cycle-Synced Channel Breakout – Detect Breakouts Confirmed by Candles and Momentum Cycles 📖 Overview The Cycle-Synced Channel Breakout indicator is a precision breakout detection tool that combines the power of: • Adaptive Keltner Channels • Dominant Cycle Period Analysis (Ehlers-inspired) • Candlestick Pattern Recognition (Engulfing) This multi-layered approach helps identify true breakout opportunities by filtering out noise and false signals, making it ideal for swing traders and intraday traders seeking high-probability directional moves. ⚙️ How It Works 1. Keltner Channel Envelope A dynamic volatility channel based on the EMA and ATR defines the upper and lower bounds of price movement. 2. Engulfing Candle Detection The script detects strong bullish and bearish engulfing patterns, which often signal trend reversals or momentum continuations. 3. Dominant Cycle Momentum (Ehlers-inspired) Using a smoothed power oscillator derived from a detrended price series, the indicator assesses whether momentum is accelerating during the breakout — filtering out weak moves. 4. Signal Confirmation Logic A signal is only shown when: • An engulfing pattern is detected, and • Price breaks out of the Keltner Channel, and • Momentum (cycle power) is rising 5. Visual Feedback • Breakout signals are plotted with “BUY” or “SELL” labels • Faded green/red background highlights confirmed breakouts • Optional display of engulfing candles with triangle markers ⸻ 🛠️ Key Features • ✅ Adaptive Keltner Channels • ✅ Bullish/Bearish Engulfing Candle Recognition • ✅ Ehlers-style Cycle Momentum Confirmation • ✅ Background highlights for confirmed breakouts • ✅ Optional candle pattern visualization • ✅ Lightweight and Pine v6 compatible ⸻ 🧪 Inputs • Keltner Length – EMA period for channel basis • Multiplier – Multiplied with ATR to determine band width • Cycle Lookback – Used to calculate smoothed cycle power • Show Engulfing Candles? – Toggles candlestick signals • Show Breakout Signals? – Toggles breakout labels and backgrounds ⸻ 🧠 How to Use • Look for “BUY” or “SELL” labels when: • An engulfing candle breaks through the Keltner Channel • Cycle momentum confirms strength behind the move • The background color will faintly highlight the breakout direction. • Use in combination with other trend or volume indicators for added confluence. 🔒 Notes • This indicator is not repainting. • It is designed for educational and research purposes only. • Works across all timeframes and asset classes (stocks, crypto, forex, etc.)
Indicador Pine Script®
por TradeTechanalysis
SuperSmoother MA OscillatorSuperSmoother MA Oscillator - Ehlers-Inspired Lag-Minimized Signal Framework Overview The SuperSmoother MA Oscillator is a crossover and momentum detection framework built on the pioneering work of John F. Ehlers, who introduced digital signal processing (DSP) concepts into technical analysis. Traditional moving averages such as SMA and EMA are prone to two persistent flaws: excessive lag, which delays recognition of trend shifts, and high-frequency noise, which produces unreliable whipsaw signals. Ehlers’ SuperSmoother filter was designed to specifically address these flaws by creating a low-pass filter with minimal lag and superior noise suppression, inspired by engineering methods used in communications and radar systems. This oscillator extends Ehlers’ foundation by combining the SuperSmoother filter with multi-length moving average oscillation, ATR-based normalization, and dynamic color coding. The result is a tool that helps traders identify market momentum, detect reliable crossovers earlier than conventional methods, and contextualize volatility and phase shifts without being distracted by transient price noise. Unlike conventional oscillators, which either oversimplify price structure or overload the chart with reactive signals, the SuperSmoother MA Oscillator is designed to balance responsiveness and stability. By preprocessing price data with the SuperSmoother filter, traders gain a signal framework that is clean, robust, and adaptable across assets and timeframes. Theoretical Foundation Traditional MA oscillators such as MACD or dual-EMA systems react to raw or lightly smoothed price inputs. While effective in some conditions, these signals are often distorted by high-frequency oscillations inherent in market data, leading to false crossovers and poor timing. The SuperSmoother approach modifies this dynamic: by attenuating unwanted frequencies, it preserves structural price movements while eliminating meaningless noise. This is particularly useful for traders who need to distinguish between genuine market cycles and random short-term price flickers. In practical terms, the oscillator helps identify: Early trend continuations (when fast averages break cleanly above/below slower averages). Preemptive breakout setups (when compressed oscillator ranges expand). Exhaustion phases (when oscillator swings flatten despite continued price movement). Its multi-purpose design allows traders to apply it flexibly across scalping, day trading, swing setups, and longer-term trend positioning, without needing separate tools for each. The oscillator’s visual system - fast/slow lines, dynamic coloration, and zero-line crossovers - is structured to provide trend clarity without hiding nuance. Strong green/red momentum confirms directional conviction, while neutral gray phases emphasize uncertainty or low conviction. This ensures traders can quickly gauge the market state without losing access to subtle structural signals. How It Works The SuperSmoother MA Oscillator builds signals through a layered process: SuperSmoother Filtering (Ehlers’ Method) At its core lies Ehlers’ two-pole recursive filter, mathematically engineered to suppress high-frequency components while introducing minimal lag. Compared to traditional EMA smoothing, the SuperSmoother achieves better spectral separation - it allows meaningful cyclical market structures to pass through, while eliminating erratic spikes and aliasing. This makes it a superior preprocessing stage for oscillator inputs. Fast and Slow Line Construction Within the oscillator framework, the filtered price series is used to build two internal moving averages: a fast line (short-term momentum) and a slow line (longer-term directional bias). These are not plotted directly on the chart - instead, their relationship is transformed into the oscillator values you see. The interaction between these two internal averages - crossovers, separation, and compression - forms the backbone of trend detection: Uptrend Signal : Fast MA rises above the slow MA with expanding distance, generating a positive oscillator swing. Downtrend Signal : Fast MA falls below the slow MA with widening divergence, producing a negative oscillator swing. Neutral/Transition : Lines compress, flattening the oscillator near zero and often preceding volatility expansion. This design ensures traders receive the information content of dual-MA crossovers while keeping the chart visually clean and focused on the oscillator’s dynamics. ATR-Based Normalization Markets vary in volatility. To ensure the oscillator behaves consistently across assets, ATR (Average True Range) normalization scales outputs relative to prevailing volatility conditions. This prevents the oscillator from appearing overly sensitive in calm markets or too flat during high-volatility regimes. Dynamic Color Coding Color transitions reflect underlying market states: Strong Green : Bullish alignment, momentum expanding. Strong Red : Bearish alignment, momentum expanding. These visual cues allow traders to quickly gauge trend direction and strength at a glance, with expanding colors indicating increasing conviction in the underlying momentum. Interpretation The oscillator offers a multi-dimensional view of price dynamics: Trend Analysis : Fast/slow line alignment and zero-line interactions reveal trend direction and strength. Expansions indicate momentum building; contractions flag weakening conditions or potential reversals. Momentum & Volatility : Rapid divergence between lines reflects increasing momentum. Compression highlights periods of reduced volatility and possible upcoming expansion. Cycle Awareness : Because of Ehlers’ DSP foundation, the oscillator captures market cycles more cleanly than conventional MA systems, allowing traders to anticipate turning points before raw price action confirms them. Divergence Detection : When oscillator momentum fades while price continues in the same direction, it signals exhaustion - a cue to tighten stops or anticipate reversals. By focusing on filtered, volatility-adjusted signals, traders avoid overreacting to noise while gaining early access to structural changes in momentum. Strategy Integration The SuperSmoother MA Oscillator adapts across multiple trading approaches: Trend Following Enter when fast/slow alignment is strong and expanding: A fast line crossing above the slow line with expanding green signals confirms bullish continuation. Use ATR-normalized expansion to filter entries in line with prevailing volatility. Breakout Trading Periods of compression often precede breakouts: A breakout occurs when fast lines diverge decisively from slow lines with renewed green/red strength. Exhaustion and Reversals Oscillator divergence signals weakening trends: Flattening momentum while price continues trending may indicate overextension. Traders can exit or hedge positions in anticipation of corrective phases. Multi-Timeframe Confluence Apply the oscillator on higher timeframes to confirm the directional bias. Use lower timeframes for refined entries during compression → expansion transitions. Technical Implementation Details SuperSmoother Algorithm (Ehlers) : Recursive two-pole filter minimizes lag while removing high-frequency noise. Oscillator Framework : Fast/slow MAs derived from filtered prices. ATR Normalization : Ensures consistent amplitude across market regimes. Dynamic Color Engine : Aligns visual cues with structural states (expansion and contraction). Multi-Factor Analysis : Combines crossover logic, volatility context, and cycle detection for robust outputs. This layered approach ensures the oscillator is highly responsive without overloading charts with noise. Optimal Application Parameters Asset-Specific Guidance: Forex : Normalize with moderate ATR scaling; focus on slow-line confirmation. Equities : Balance responsiveness with smoothing; useful for capturing sector rotations. Cryptocurrency : Higher ATR multipliers recommended due to volatility. Futures/Indices : Lower frequency settings highlight structural trends. Timeframe Optimization: Scalping (1-5min) : Higher sensitivity, prioritize fast-line signals. Intraday (15m-1h) : Balance between fast/slow expansions. Swing (4h-Daily) : Focus on slow-line momentum with fast-line timing. Position (Daily-Weekly) : Slow lines dominate; fast lines highlight cycle shifts. Performance Characteristics High Effectiveness: Trending environments with moderate-to-high volatility. Assets with steady liquidity and clear cyclical structures. Reduced Effectiveness: Flat/choppy conditions with little directional bias. Ultra-short timeframes (<1m), where noise dominates. Integration Guidelines Confluence : Combine with liquidity zones, order blocks, and volume-based indicators for confirmation. Risk Management : Place stops beyond slow-line thresholds or ATR-defined zones. Dynamic Trade Management : Use expansions/contractions to scale position sizes or tighten stops. Multi-Timeframe Confirmation : Filter lower-timeframe entries with higher-timeframe momentum states. Disclaimer The SuperSmoother MA Oscillator is an advanced trend and momentum analysis tool, not a guaranteed profit system. Its effectiveness depends on proper parameter settings per asset and disciplined risk management. Traders should use it as part of a broader technical framework and not in isolation.
Indicador Pine Script®
por BOSWaves
8
Logit Transform -EasyNeuro-Logit Transform This script implements a novel indicator inspired by the Fisher Transform, replacing its core arctanh-based mapping with the logit transform. It is designed to highlight extreme values in bounded inputs from a probabilistic and statistical perspective. Background: Fisher Transform The Fisher Transform, introduced by John Ehlers , is a statistical technique that maps a bounded variable x (between a and b) to a variable approximately following a Gaussian distribution. The standard form for a normalized input y (between -1 and 1) is F(y) = 0.5 * ln((1 + y)/(1 - y)) = arctanh(y). This transformation has the following properties: Linearization of extremes: Small deviations around the mean are smooth, while movements near the boundaries are sharply amplified. Gaussian approximation: After transformation, the variable approximates a normal distribution, enabling analytical techniques that assume normality. Probabilistic interpretation: The Fisher Transform can be linked to likelihood ratio tests, where the transform emphasizes deviations from median or expected values in a statistically meaningful way. In technical analysis, this allows traders to detect turning points or extreme market conditions more clearly than raw oscillators alone. Logit Transform as a Generalization The logit function is defined for p between 0 and 1 as logit(p) = ln(p / (1 - p)). Key properties of the logit transform: Maps probabilities in (0, 1) to the entire real line, similar to the Fisher Transform. Emphasizes values near 0 and 1, providing sharp differentiation of extreme states. Directly interpretable in terms of odds and likelihood ratios: logit(p) = ln(odds). From a statistical viewpoint, the logit transform corresponds to the canonical link function in binomial generalized linear models (GLMs). This provides a natural interpretation of the transformed variable as the logarithm of the likelihood ratio between success and failure states, giving a rigorous probabilistic framework for extreme value detection. Theoretical Advantages Distributional linearization: For inputs that can be interpreted as probabilities, the logit transform creates a variable approximately linear in log-odds, similar to Fisher’s goal of Gaussianization but with a probabilistic foundation. Extreme sensitivity: By amplifying small differences near 0 or 1, it allows for sharper detection of market extremes or overbought/oversold conditions. Statistical interpretability: Provides a link to statistical hypothesis testing via likelihood ratios, enabling integration with probabilistic models or risk metrics. Applications in Technical Analysis Oscillator enhancement: Apply to RSI, Stochastic Oscillators, or other bounded indicators to accentuate extreme values with a well-defined probabilistic interpretation. Comparative study: Use alongside the Fisher Transform to analyze the effect of different nonlinear mappings on market signals, helping to uncover subtle nonlinearity in price behavior. Probabilistic risk assessment: Transforming input series into log-odds allows incorporation into statistical risk models or volatility estimation frameworks. Practical Considerations The logit diverges near 0 and 1, requiring careful scaling or smoothing to avoid numerical instability. As with the Fisher Transform, this indicator is not a standalone trading signal and should be combined with complementary technical or statistical indicators. In summary, the Logit Transform builds upon the Fisher Transform’s theoretical foundation while introducing a probabilistically rigorous mapping. By connecting extreme-value detection to odds ratios and likelihood principles, it provides traders and analysts with a mathematically grounded tool for examining market dynamics.
Indicador Pine Script®
por EazyNeuro
TASC 2025.09 The Continuation Index █ OVERVIEW This script implements the "Continuation Index" as described by John F. Ehlers in the September 2025 edition of TASC's Trader's Tips . The Continuation Index uses Laguerre filters (featured in the July 2025 edition) to provide an early indication of trend direction, continuation, and exhaustion. █ CONCEPTS The idea for the Continuation Index was formed from an observation about Laguerre filters. In his article, Ehlers notes that when price is in trend, it tends to stay to one side of the filter. When considering smoothing, the UltimateSmoother was an obvious choice to reduce lag. With that in mind, The Continuation Index normalizes the difference between UltimateSmoother and the Laguerre filter to produce a two-state oscillator. To minimize lag, the UltimateSmoother length in this indicator is fixed to half the length of the Laguerre filter. █ USAGE The Continuation Index consists of two primary states. +1 suggests that the trader should position on the long side. -1 suggests that the user should position on the short side. Other readings can imply other opportunities, such as: High Value Fluctuation could be used as a "buy the dip" opportunity. Low Value Fluctuation could be used as a "sell the pop" opportunity. █ INPUTS By understanding the inputs and adjusting them as needed, each trader can benefit more from this indicator: Gamma : Controls the Laguerre filter's response. This can be set anywhere between 0 and 1. If set to 0, the filter’s value will be the same as the UltimateSmoother. Order : Controls the lag of the Laguerre filter, which is important when considering the timing of the system for spotting reversals. This can be set from 1 to 10, with lower values typically producing faster timing. Length : Affects the smoothing of the display. Ehlers recommends starting with this value set to the intended amount of time you plan to hold a position. Consider your chart timeframe when setting this input. For example, on a daily chart, if you intend to hold a position for one month, set a value of 20.
Indicador Pine Script®
por PineCodersTASC
7
TASC 2025.07 Laguerre Filters█ OVERVIEW This script implements the Laguerre filter and oscillator described by John F. Ehlers in the article "A Tool For Trend Trading, Laguerre Filters" from the July 2025 edition of TASC's Traders' Tips . The new Laguerre filter utilizes the UltimateSmoother filter in place of an exponential moving average (EMA) in its calculation, offering improved responsiveness and reduced lag. █ CONCEPTS As Ehlers explains in his article, the Laguerre filter is a form of transversal filter . A transversal filter calculates an output signal using a tapped delay line . It creates multiple delayed versions of an input signal, applies weight to each delay, and then calculates their sum to generate the filtered result. The Laguerre filter's structure relies on Laguerre polynomials — solutions to a differential equation solved by Edmond Laguerre in the 1800s. When Ehlers analyzed the formula for these polynomials on discrete systems (e.g., financial time series), he found that the first term's expression corresponds to an EMA response, and all subsequent terms correspond to an all-pass response. In contrast to other filter types, an all-pass filter produces phase shift (i.e., delay) in an input signal's components without affecting its amplitude. Ehlers observed that these characteristics of Laguerre polynomials make them suitable for use in a transversal filter structure, and thus the Laguerre filter was born. However, he notes that EMAs are not great filters in general. As such, to improve on the Laguerre filter's design, Ehlers modified it by replacing the EMA term with his UltimateSmoother filter. The resulting Laguerre filter has significantly reduced lag, achieving a tighter response to market fluctuations while maintaining smoothness. Ehlers suggests that traders can analyze crossings between the UltimateSmoother and this Laguerre filter, or those between two Laguerre filters of different order, for helpful buy and sell signals. In addition to the Laguerre filter, Ehlers derived a smooth, low-lag oscillator based on the difference between the first and second terms in the modified filter structure, scaled by the root mean square (RMS). The resulting oscillator provides an alternative filtered representation of market data, which can help traders identify swing and mean-reversion signals. █ USAGE This indicator calculates both the Laguerre filter and the Laguerre oscillator described in Ehlers' article. It displays the Laguerre filter on the main chart pane and the oscillator in a separate pane. Users can control the behavior of the filter and oscillator with the inputs in the "Settings/Inputs" tab: The "Period" input defines the critical period of the UltimateSmoother used in the Laguerre filter and oscillator calculations. Its default value is 30. The "Gamma" input determines the weighting behavior of the Laguerre filter and oscillator. It accepts a positive value between 0 and 1. Use a lower value for quicker responsiveness to market changes, and a higher value for trends. The default value is 0.5. The "RMS length" input determines the length of the RMS calculation for oscillator normalization. The default value is 100 bars.
Indicador Pine Script®
por PineCodersTASC
13
Ehlers Ultimate Bands (UBANDS)UBANDS: ULTIMATE BANDS 🔍 OVERVIEW AND PURPOSE Ultimate Bands, developed by John F. Ehlers, are a volatility-based channel indicator designed to provide a responsive and smooth representation of price boundaries with significantly reduced lag compared to traditional Bollinger Bands. Bollinger Bands typically use a Simple Moving Average for the centerline and standard deviations from it to establish the bands, both of which can increase lag. Ultimate Bands address this by employing Ehlers' Ultrasmooth Filter for the central moving average. The bands are then plotted based on the volatility of price around this ultrasmooth centerline. The primary purpose of Ultimate Bands is to offer traders a clearer view of potential support and resistance levels that react quickly to price changes while filtering out excessive noise, aiming for nearly zero lag in the indicator band. 🧩 CORE CONCEPTS Ultrasmooth Centerline: Employs the Ehlers Ultrasmooth Filter as the basis (centerline) for the bands, aiming for minimal lag and enhanced smoothing. Volatility-Adaptive Width: The distance between the upper and lower bands is determined by a measure of price deviation from the ultrasmooth centerline. This causes the bands to widen during volatile periods and contract during calm periods. Dynamic Support/Resistance: The bands serve as dynamic levels of potential support (lower band) and resistance (upper band). 🧮 CALCULATION AND MATHEMATICAL FOUNDATION Ehlers' Original Concept for Deviation: John Ehlers describes the deviation calculation as: "The deviation at each data sample is the difference between Smooth and the Close at that data point. The Standard Deviation (SD) is computed as the square root of the average of the squares of the individual deviations." This describes calculating the Root Mean Square (RMS) of the residuals: Smooth = UltrasmoothFilter(Source, Length) Residuals = Source - Smooth SumOfSquaredResiduals = Sum(Residuals ^2) for i over Length MeanOfSquaredResiduals = SumOfSquaredResiduals / Length SD_Ehlers = SquareRoot(MeanOfSquaredResiduals) (This is the RMS of residuals) Pine Script Implementation's Deviation: The provided Pine Script implementation calculates the statistical standard deviation of the residuals: Smooth = UltrasmoothFilter(Source, Length) (referred to as _ehusf in the script) Residuals = Source - Smooth Mean_Residuals = Average(Residuals, Length) Variance_Residuals = Average((Residuals - Mean_Residuals)^2, Length) SD_Pine = SquareRoot(Variance_Residuals) (This is the statistical standard deviation of residuals) Band Calculation (Common to both approaches, using their respective SD): UpperBand = Smooth + (NumSDs × SD) LowerBand = Smooth - (NumSDs × SD) 🔍 Technical Note: The Pine Script implementation uses a statistical standard deviation of the residuals (differences between price and the smooth average). Ehlers' original text implies an RMS of these residuals. While both measure dispersion, they will yield slightly different values. The Ultrasmooth Filter itself is a key component, designed for responsiveness. 📈 INTERPRETATION DETAILS Reduced Lag: The primary advantage is the significant reduction in lag compared to standard Bollinger Bands, allowing for quicker reaction to price changes. Volatility Indication: Widening bands indicate increasing market volatility, while narrowing bands suggest decreasing volatility. Overbought/Oversold Conditions (Use with caution): • Price touching or exceeding the Upper Band may suggest overbought conditions. • Price touching or falling below the Lower Band may suggest oversold conditions. Trend Identification: • Price consistently "walking the band" (moving along the upper or lower band) can indicate a strong trend. • The Middle Band (Ultrasmooth Filter) acts as a dynamic support/resistance level and indicates the short-term trend direction. Comparison to Ultimate Channel: Ehlers notes that the Ultimate Band indicator does not differ from the Ultimate Channel indicator in any major fashion. 🛠️ USE AND APPLICATION Ultimate Bands can be used similarly to how Keltner Channels or Bollinger Bands are used for interpreting price action, with the main difference being the reduced lag. Example Trading Strategy (from John F. Ehlers): Hold a position in the direction of the Ultimate Smoother (the centerline). Exit that position when the price "pops" outside the channel or band in the opposite direction of the trade. This is described as a trend-following strategy with an automatic following stop. ⚠️ LIMITATIONS AND CONSIDERATIONS Lag (Minimized but Present): While significantly reduced, some minimal lag inherent to averaging processes will still exist. Increasing the Length parameter for smoother bands will moderately increase this lag. Parameter Sensitivity: The Length and StdDev Multiplier settings are key to tuning the indicator for different assets and timeframes. False Signals: As with any band indicator, false signals can occur, particularly in choppy or non-trending markets. Not a Standalone System: Best used in conjunction with other forms of analysis for confirmation. Deviation Calculation Nuance: Be aware of the difference in deviation calculation (statistical standard deviation vs. RMS of residuals) if comparing directly to Ehlers' original concept as described. 📚 REFERENCES Ehlers, J. F. (2024). Article/Publication where "Code Listing 2" for Ultimate Bands is featured. (Specific source to be identified if known, e.g., "Stocks & Commodities Magazine, Vol. XX, No. YY"). Ehlers, J. F. (General). Various publications on advanced filtering and cycle analysis. (e.g., "Rocket Science for Traders", "Cycle Analytics for Traders").
Indicador Pine Script®
por mihakralj
TASC 2025.06 Cybernetic Oscillator█ OVERVIEW This script implements the Cybernetic Oscillator introduced by John F. Ehlers in his article "The Cybernetic Oscillator For More Flexibility, Making A Better Oscillator" from the June 2025 edition of the TASC Traders' Tips . It cascades two-pole highpass and lowpass filters, then scales the result by its root mean square (RMS) to create a flexible normalized oscillator that responds to a customizable frequency range for different trading styles. █ CONCEPTS Oscillators are indicators widely used by technical traders. These indicators swing above and below a center value, emphasizing cyclic movements within a frequency range. In his article, Ehlers explains that all oscillators share a common characteristic: their calculations involve computing differences . The reliance on differences is what causes these indicators to oscillate about a central point. The difference between two data points in a series acts as a highpass filter — it allows high frequencies (short wavelengths) to pass through while significantly attenuating low frequencies (long wavelengths). Ehlers demonstrates that a simple difference calculation attenuates lower-frequency cycles at a rate of 6 dB per octave. However, the difference also significantly amplifies cycles near the shortest observable wavelength, making the result appear noisier than the original series. To mitigate the effects of noise in a differenced series, oscillators typically smooth the series with a lowpass filter, such as a moving average. Ehlers highlights an underlying issue with smoothing differenced data to create oscillators. He postulates that market data statistically follows a pink spectrum , where the amplitudes of cyclic components in the data are approximately directly proportional to the underlying periods. Specifically, he suggests that cyclic amplitude increases by 6 dB per octave of wavelength. Because some conventional oscillators, such as RSI, use differencing calculations that attenuate cycles by only 6 dB per octave, and market cycles increase in amplitude by 6 dB per octave, such calculations do not have a tangible net effect on larger wavelengths in the analyzed data. The influence of larger wavelengths can be especially problematic when using these oscillators for mean reversion or swing signals. For instance, an expected reversion to the mean might be erroneous because oscillator's mean might significantly deviate from its center over time. To address the issues with conventional oscillator responses, Ehlers created a new indicator dubbed the Cybernetic Oscillator. It uses a simple combination of highpass and lowpass filters to emphasize a specific range of frequencies in the market data, then normalizes the result based on RMS. The process is as follows: Apply a two-pole highpass filter to the data. This filter's critical period defines the longest wavelength in the oscillator's passband. Apply a two-pole SuperSmoother (lowpass filter) to the highpass-filtered data. This filter's critical period defines the shortest wavelength in the passband. Scale the resulting waveform by its RMS. If the filtered waveform follows a normal distribution, the scaled result represents amplitude in standard deviations. The oscillator's two-pole filters attenuate cycles outside the desired frequency range by 12 dB per octave. This rate outweighs the apparent rate of amplitude increase for successively longer market cycles (6 dB per octave). Therefore, the Cybernetic Oscillator provides a more robust isolation of cyclic content than conventional oscillators. Best of all, traders can set the periods of the highpass and lowpass filters separately, enabling fine-tuning of the frequency range for different trading styles. █ USAGE The "Highpass period" input in the "Settings/Inputs" tab specifies the longest wavelength in the oscillator's passband, and the "Lowpass period" input defines the shortest wavelength. The oscillator becomes more responsive to rapid movements with a smaller lowpass period. Conversely, it becomes more sensitive to trends with a larger highpass period. Ehlers recommends setting the smallest period to a value above 8 to avoid aliasing. The highpass period must not be smaller than the lowpass period. Otherwise, it causes a runtime error. The "RMS length" input determines the number of bars in the RMS calculation that the indicator uses to normalize the filtered result. This indicator also features two distinct display styles, which users can toggle with the "Display style" input. With the "Trend" style enabled, the indicator plots the oscillator with one of two colors based on whether its value is above or below zero. With the "Threshold" style enabled, it plots the oscillator as a gray line and highlights overbought and oversold areas based on the user-specified threshold. Below, we show two instances of the script with different settings on an equities chart. The first uses the "Threshold" style with default settings to pass cycles between 20 and 30 bars for mean reversion signals. The second uses a larger highpass period of 250 bars and the "Trend" style to visualize trends based on cycles spanning less than one year:
Indicador Pine Script®
por PineCodersTASC
13
Ehlers Regime Dynamic CandlesCore Calculation Mechanism The indicator uses advanced Ehlers signal processing techniques to identify market regimes and create dynamically colored candles that reflect market conditions. Super Smoother Filter: Price data (open, high, low, close) is processed through an Ehlers Super Smoother Filter to reduce market noise while preserving important price movements. This creates a clearer signal for regime detection. Autocorrelation Analysis: The core of regime detection uses autocorrelation functions at different lag periods: Primary autocorrelation measures correlation between the current price and its previous value Trending autocorrelation measures longer-term persistence in the data series These values combined determine if the market is in a trending or choppy regime (Image showing Ehlers custom candles vs default candlesticks) Regime Strength Calculation: -Raw signal from autocorrelation with user-defined threshold adjustment -Adaptive scaling based on sensitivity parameter -Optional volume validation that confirms signal strength using volume data -Normalization to 0-1 range and smoothing for visual consistency -Percentile ranking to provide contextually meaningful strength values Fisher Transform: Applied to the smoothed price to identify statistical extremes, which helps adjust transparency levels during significant price movements. Key Features & Components Regime Detection: Identifies trending vs. choppy market conditions using Ehlers' autocorrelation techniques. Dynamic Candle Coloring: Candles transition smoothly between three color states: Bullish trending (typically green/teal) Bearish trending (typically red/purple) Choppy/neutral (typically blue/silver) Volume Validation: Optional incorporation of volume data to confirm trend strength (stronger volume during trending periods increases confidence). Adaptive Transparency: Candles become more opaque during statistically significant price movements based on Fisher Transform values. Gradient Smoothing: Controls the visual transition between regime states for a more aesthetically pleasing appearance. Customizable Colors and Style: Full control over all visual aspects including candle body/wick colors and transparency. Configuration Options Users can adjust the following parameters in the indicator settings: Main Settings: Cycle Length: Controls the lookback period for cycle detection. Lower values increase responsiveness but may introduce noise. Gradient Smoothness: Determines how quickly colors transition when regime changes. Trend Detection Threshold: Sets the autocorrelation strength required to classify a trend. Trend Sensitivity: Scales regime strength calculation to produce a better distribution of values. Use Volume: Toggles whether volume data is used to validate trend strength. Color Settings: Trending Regime Colors: Separate color options for bullish and bearish candle bodies and wicks. Choppy Regime Colors: Color options for candle bodies and wicks during sideways/neutral markets. Style Settings: Candle Border Options: Toggle borders and adjust their color and transparency. Adaptive Transparency: Enable/disable dynamic transparency based on statistical significance. Base Transparency: Set the baseline transparency level for all candles. Interpretation Notes Color Transitions: As the market shifts between regimes, candle colors gradually transition, providing visual cues about market structure changes. Regime Strength: The intensity of colors indicates the strength of the detected regime: Strong trending regimes show vibrant trending colors Weak or mixed regimes display colors closer to the choppy/neutral color Transitions between regimes show gradient colors Transparency Changes: More opaque candles indicate statistically significant price movements, while more transparent candles suggest routine or less significant price action. Volume Interaction: When volume validation is enabled, trending colors become more pronounced during high volume trends and subdued during low volume periods. Disclaimer: These are custom candles that are significantly different from normal candlesticks. Unlike traditional candlesticks that display raw price data, these candles: • Use Ehlers signal processing to filter and smooth price data • Dynamically change color based on detected market regimes • Show statistical significance through transparency • May appear delayed compared to standard candles due to the filtering process Traditional trading strategies dependent on candlestick patterns will not work with these. Risk Disclaimer Trading involves significant risk. This indicator is provided for analytical purposes only and does not constitute financial advice. Past performance is not indicative of future results. Use sound risk management practices and never trade with capital you cannot afford to lose. The Ehlers Regime Dynamic Candles indicator should be used as part of a comprehensive trading approach, not as a standalone trading system.
Indicador Pine Script®
por sizzlinsoft
1
Ehlers Adaptive RSIThe Ehlers Adaptive RSI improves on the traditional RSI by dynamically adjusting its period based on market conditions. Problem with the Classic RSI: The traditional Relative Strength Index (RSI) uses a fixed period (e.g., 14), making it slow to react in volatile markets and too sensitive in stable conditions. How the Adaptive RSI Solves This: Instead of a fixed period, this version automatically adapts based on market volatility using a combination of ATR (Average True Range) and EMA (Exponential Moving Average). Key Benefits: More Responsive – Quickly adapts to market shifts, reducing lag. Less Noise – Filters out unnecessary fluctuations in stable trends. Self-Adjusting – No need to manually change RSI settings for different market conditions. Better Signal Accuracy – Helps detect real trend reversals without false alarms. This script is for informational and educational purposes only. It does not constitute financial advice, and past performance does not guarantee future results. Use it at your own risk.
Indicador Pine Script®
por Julien_Exe
6
Hull Moving Average Adaptive RSI (Ehlers)Hull Moving Average Adaptive RSI (Ehlers) The Hull Moving Average Adaptive RSI (Ehlers) is an enhanced trend-following indicator designed to provide a smooth and responsive view of price movement while incorporating an additional momentum-based analysis using the Adaptive RSI. Principle and Advantages of the Hull Moving Average: - The Hull Moving Average (HMA) is known for its ability to track price action with minimal lag while maintaining a smooth curve. - Unlike traditional moving averages, the HMA significantly reduces noise and responds faster to market trends, making it highly effective for detecting trend direction and changes. - It achieves this by applying a weighted moving average calculation that emphasizes recent price movements while smoothing out fluctuations. Why the Adaptive RSI Was Added: - The core HMA line remains the foundation of the indicator, but an additional analysis using the Adaptive RSI has been integrated to provide more meaningful insights into momentum shifts. - The Adaptive RSI is a modified version of the traditional Relative Strength Index that dynamically adjusts its sensitivity based on market volatility. - By incorporating the Adaptive RSI, the HMA visually represents whether momentum is strengthening or weakening, offering a complementary layer of analysis. How the Adaptive RSI Influences the Indicator: - High Adaptive RSI (above 65): The market may be overbought, or bullish momentum could be fading. The HMA turns shades of red, signaling a possible exhaustion phase or potential reversals. - Neutral Adaptive RSI (around 50): The market is in a balanced state, meaning neither buyers nor sellers are in clear control. The HMA takes on grayish tones to indicate this consolidation. - Low Adaptive RSI (below 35): The market may be oversold, or bearish momentum could be weakening. The HMA shifts to shades of blue, highlighting potential recovery zones or trend slowdowns. Why This Combination is Powerful: - While the HMA excels in tracking trends and reducing lag, it does not provide information about momentum strength on its own. - The Adaptive RSI bridges this gap by adding a clear visual layer that helps traders assess whether a trend is likely to continue, consolidate, or reverse. - This makes the indicator particularly useful for spotting trend exhaustion and confirming momentum shifts in real-time. Best Use Cases: - Works effectively on timeframes from 1 hour (1H) to 1 day (1D), making it suitable for swing trading and position trading. - Particularly useful for trading indices (SPY), stocks, forex, and cryptocurrencies, where momentum shifts are frequent. - Helps identify not just trend direction but also whether that trend is gaining or losing strength. Recommended Complementary Indicators: - Adaptive Trend Finder: Helps identify the dominant long-term trend. - Williams Fractals Ultimate: Provides key reversal points to validate trend shifts. - RVOL (Relative Volume): Confirms significant moves based on volume strength. This enhanced HMA with Adaptive RSI provides a powerful, intuitive visual tool that makes trend analysis and momentum interpretation more effective and efficient. This indicator is for educational and informational purposes only. It should not be considered financial advice or a guarantee of performance. Always conduct your own research and use proper risk management when trading. Past performance does not guarantee future results.
Indicador Pine Script®
por Julien_Exe
1
TASC 2025.04 The Ultimate Oscillator█ OVERVIEW This script implements an alternative, refined version of the Ultimate Oscillator (UO) designed to reduce lag and enhance responsiveness in momentum indicators, as introduced by John F. Ehlers in his article "Less Lag In Momentum Indicators, The Ultimate Oscillator" from the April 2025 edition of TASC's Traders' Tips . █ CONCEPTS In his article, Ehlers states that indicators are essentially filters that remove unwanted noise (i.e., unnecessary information) from market data. Simply put, they process a series of data to place focus on specific information, providing a different perspective on price dynamics. Various filter types attenuate different periodic signals within the data. For instance, a lowpass filter allows only low-frequency signals, a highpass filter allows only high-frequency signals, and a bandpass filter allows signals within a specific frequency range . Ehlers explains that the key to removing indicator lag is to combine filters of different types in such a way that the result preserves necessary, useful signals while minimizing delay (lag). His proposed UltimateOscillator aims to maintain responsiveness to a specific frequency range by measuring the difference between two highpass filters' outputs. The oscillator uses the following formula: UO = (HP1 - HP2) / RMS Where: HP1 is the first highpass filter. HP2 is another highpass filter that allows only shorter wavelengths than the critical period of HP1. RMS is the root mean square of the highpass filter difference, used as a scaling factor to standardize the output. The resulting oscillator is similar to a bandpass filter , because it emphasizes wavelengths between the critical periods of the two highpass filters. Ehlers' UO responds quickly to value changes in a series, providing a responsive view of momentum with little to no lag. █ USAGE Ehlers' UltimateOscillator sets the critical periods of its highpass filters using two parameters: BandEdge and Bandwidth : The BandEdge sets the critical period of the second highpass filter, which determines the shortest wavelengths in the response. The Bandwidth is a multiple of the BandEdge used for the critical period of the first highpass filter, which determines the longest wavelengths in the response. Ehlers suggests that a Bandwidth value of 2 works well for most applications. However, traders can use any value above or equal to 1.4. Users can customize these parameters with the "Bandwidth" and "BandEdge" inputs in the "Settings/Inputs" tab. The script plots the UO calculated for the specified "Source" series in a separate pane, with a color based on the chart's foreground color. Positive UO values indicate upward momentum or trends, and negative UO values indicate the opposite. Additionally, this indicator provides the option to display a "cloud" from 10 additional UO series with different settings for an aggregate view of momentum. The "Cloud" input offers four display choices: "Bandwidth", "BandEdge", "Bandwidth + BandEdge", or "None". The "Bandwidth" option calculates oscillators with different Bandwidth values based on the main oscillator's setting. Likewise, the "BandEdge" option calculates oscillators with varying BandEdge values. The "Bandwidth + BandEdge" option calculates the extra oscillators with different values for both parameters. When a user selects any of these options, the script plots the maximum and minimum oscillator values and fills their space with a color gradient. The fill color corresponds to the net sum of each UO's sign , indicating whether most of the UOs reflect positive or negative momentum. Green hues mean most oscillators are above zero, signifying stronger upward momentum. Red hues mean most are below zero, indicating stronger downward momentum.
Indicador Pine Script®
por PineCodersTASC
6
[GYTS] Ultimate Smoother (3-poles + 2 poles)Ultimate Smoother (3-pole) 🌸 Part of GoemonYae Trading System (GYTS) 🌸 🌸 --------- INTRODUCTION --------- 🌸 💮 Release of 3-Pole Ultimate Smoother This indicator presents a new 3-pole version of John Ehlers' Ultimate Smoother (2024) . This results in an unconventional filter that exhibits effectively zero lag in practical trading applications, regardless of the set period. By using a 2-pole high-pass filter in its design, it responds to price direction changes on the same bar, while still allowing the user to control smoothness. 💮 What is the Ultimate Smoother? The original Ultimate Smoother is a revolutionary filter designed by John Ehlers (2024) that smooths price data with virtually zero lag in the pass band. While conventional filters always introduce lag when removing market noise, the Ultimate Smoother maintains phase alignment at low frequencies while still providing excellent noise reduction. 💮 Mathematical Foundation The Ultimate Smoother achieves its remarkable properties through a clever mathematical approach: 1. Instead of directly designing a low-pass filter (like traditional moving averages), it subtracts a high-pass filter from an all-pass filter (the original input data). 2. At very low frequencies, the high-pass filter contributes almost nothing, so the output closely matches the input in both amplitude and phase. 3. At higher frequencies, the high-pass filter's response increasingly matches the input data, resulting in cancellation through subtraction. The 3-pole version extends this principle by using a higher-order high-pass filter, requiring additional coefficients and handling more terms in the numerator of the transfer function. 🌸 --------- USAGE GUIDE --------- 🌸 💮 Period Parameter Behaviour The period parameter in the 3-pole Ultimate Smoother works somewhat counterintuitively: - Longer periods: Result in less smooth, but more responsive following of the price. The filter output more closely tracks the input data. - Shorter periods: Produce smoother output but may exhibit overshooting (extrapolating price movement) for larger movements. This is different from most filters where longer periods typically produce smoother outputs with more lag. 💮 When to Choose 3-Pole vs. 2-Pole - Choose the 3-pole version when you need zero-lag but want to control the smoothness - Choose the 2-pole version when you are okay with some lag with the benefit of more smoothness. 🌸 --------- ACKNOWLEDGEMENTS --------- 🌸 This indicator builds upon the pioneering work of John Ehlers, particularly from his article April 2024 edition of TASC's Traders' Tips . The original version is published on TradingView by @PineCodersTASC . This 3-pole extension was developed by @GoemonYae . Feedback is highly appreciated!
Indicador Pine Script®
por GoemonYae
Ehlers Stable Dominant Cycle Length [graylange]Stable Dominant Cycle Length – Adaptive Cycle Detection for Market Timing This script calculates the dominant cycle length of the market using an improved version of John Ehlers' Hilbert Transform approach. Unlike traditional implementations, this version includes advanced smoothing techniques to reduce noise and prevent erratic spikes, making it more reliable for adaptive cycle-based strategies. 🔥 Key Features: ✅ Noise-Reduced Cycle Detection – Uses a Weighted Moving Average (WMA) detrending method instead of raw Hilbert Transform values to enhance stability. ✅ Adaptive Smoothing – Applies an Exponential Moving Average (EMA) to the instantaneous period, reducing excessive volatility in cycle length calculations. ✅ Phase Wrapping & Constraints – Clamps phase changes to prevent unrealistic cycle swings and division errors. ✅ Dynamic Cycle Adjustment – The dominant cycle length updates in real time, constrained within a reasonable range (6 to 50 bars) to avoid extreme peaks. 📌 How to Use It: Identify Market Cycles – Use the dominant cycle length to determine optimal trend-following vs. mean-reversion strategies. Enhance MESA Filters – Apply the detected cycle length to adjust Ehlers’ MESA Adaptive Moving Average (MAMA) dynamically. Fine-Tune Alpha Settings – Reduce overfitting in cycle-based indicators by basing parameters on a stable dominant cycle estimate.
Indicador Pine Script®
por nglange3
1
TASC 2025.02 Autocorrelation Indicator█ OVERVIEW This script implements the Autocorrelation Indicator introduced by John Ehlers in the "Drunkard's Walk: Theory And Measurement By Autocorrelation" article from the February 2025 edition of TASC's Traders' Tips . The indicator calculates the autocorrelation of a price series across several lags to construct a periodogram , which traders can use to identify market cycles, trends, and potential reversal patterns. █ CONCEPTS Drunkard's walk A drunkard's walk , formally known as a random walk , is a type of stochastic process that models the evolution of a system or variable through successive random steps. In his article, John Ehlers relates this model to market data. He discusses two first- and second-order partial differential equations, modified for discrete (non-continuous) data, that can represent solutions to the discrete random walk problem: the diffusion equation and the wave equation. According to Ehlers, market data takes on a mixture of two "modes" described by these equations. He theorizes that when "diffusion mode" is dominant, trading success is almost a matter of luck, and when "wave mode" is dominant, indicators may have improved performance. Pink spectrum John Ehlers explains that many recent academic studies affirm that market data has a pink spectrum , meaning the power spectral density of the data is proportional to the wavelengths it contains, like pink noise . A random walk with a pink spectrum suggests that the states of the random variable are correlated and not independent. In other words, the random variable exhibits long-range dependence with respect to previous states. Autocorrelation function (ACF) Autocorrelation measures the correlation of a time series with a delayed copy, or lag , of itself. The autocorrelation function (ACF) is a method that evaluates autocorrelation across a range of lags , which can help to identify patterns, trends, and cycles in stochastic market data. Analysts often use ACF to detect and characterize long-range dependence in a time series. The Autocorrelation Indicator evaluates the ACF of market prices over a fixed range of lags, expressing the results as a color-coded heatmap representing a dynamic periodogram. Ehlers suggests the information from the periodogram can help traders identify different market behaviors, including: Cycles : Distinguishable as repeated patterns in the periodogram. Reversals : Indicated by sharp vertical changes in the periodogram when the indicator uses a short data length . Trends : Indicated by increasing correlation across lags, starting with the shortest, over time. █ USAGE This script calculates the Autocorrelation Indicator on an input "Source" series, smoothed by Ehlers' UltimateSmoother filter, and plots several color-coded lines to represent the periodogram's information. Each line corresponds to an analyzed lag, with the shortest lag's line at the bottom of the pane. Green hues in the line indicate a positive correlation for the lag, red hues indicate a negative correlation (anticorrelation), and orange or yellow hues mean the correlation is near zero. Because Pine has a limit on the number of plots for a single indicator, this script divides the periodogram display into three distinct ranges that cover different lags. To see the full periodogram, add three instances of this script to the chart and set the "Lag range" input for each to a different value, as demonstrated in the chart above. With a modest autocorrelation length, such as 20 on a "1D" chart, traders can identify seasonal patterns in the price series, which can help to pinpoint cycles and moderate trends. For instance, on the daily ES1! chart above, the indicator shows repetitive, similar patterns through fall 2023 and winter 2023-2024. The green "triangular" shape rising from the zero lag baseline over different time ranges corresponds to seasonal trends in the data. To identify turning points in the price series, Ehlers recommends using a short autocorrelation length, such as 2. With this length, users can observe sharp, sudden shifts along the vertical axis, which suggest potential turning points from upward to downward or vice versa.
Indicador Pine Script®
por PineCodersTASC
8
Ehlers Maclaurin Ultimate Smoother [CT]Ehlers Maclaurin Ultimate Smoother Introduction The Ehlers Maclaurin Ultimate Smoother is an innovative enhancement of the classic Ehlers SuperSmoother. By leveraging advanced Maclaurin series approximations, this indicator offers superior market analysis and signal generation. The indicator combines Ehlers' Ultimate Smoother with Maclaurin series approximations to create a more efficient and accurate smoothing mechanism: Input price data passes through the initial smoothing phase Maclaurin series approximates trigonometric functions Enhanced high-pass filter removes market noise Final smoothing phase produces the output signal Why the Maclaurin Approach? The Maclaurin series is a special form of the Taylor series, centered around 0. It provides an efficient way to approximate complex functions using polynomial terms. In this indicator, we use the Maclaurin approach to improve the sine and cosine functions, resulting in: Faster Calculations: By using polynomial approximations, we significantly reduce computational complexity. Improved Stability: The approximation provides a more stable numerical basis for calculations. Preservation of Precision: Despite the approximation, we maintain the precision needed for price smoothing. Calculations The indicator employs several key mathematical components: Maclaurin Series Approximation: sin(x) ≈ x - x³/3! + x⁵/5! - x⁷/7! + x⁹/9! cos(x) ≈ 1 - x²/2! + x⁴/4! - x⁶/6! + x⁸/8! Smoothing Algorithm: Uses exponential smoothing with optimized coefficients Implements high-pass filtering for noise reduction Applies dynamic weighting based on market conditions Mathematical Foundation Utilizes Maclaurin series for trigonometric approximation Implements Ehlers' smoothing principles Incorporates advanced filtering techniques Technical Advantages Signal Processing: Lag Reduction: Faster signal detection with less delay. Noise Filtration: Effective elimination of high-frequency noise. Precision Enhancement: Preservation of critical price movements. Adaptive Processing: Dynamic response to market volatility. Visual Enhancements: Smart color intensity mapping. Real-time visualization of trend strength. Adaptive opacity based on movement significance. Implementation Core Configuration: Plot Type: Choose between the original and the Maclaurin enhanced version. Length: Default set to 30, optimal for daily timeframes. hpLength: Default set to 10 for enhanced noise reduction. Advanced Parameters: The indicator offers advanced control with: Dual processing modes (Original/Maclaurin). Dynamic color intensity system. Customizable smoothing parameters. Professional Analysis Tools: Accurate trend reversal identification. Advanced support/resistance detection. Superior performance in volatile markets. Technical Specifications Maclaurin Series Implementation: The indicator employs a 5-term Maclaurin series approximation for both sine and cosine, ensuring efficient and accurate computation. Performance Metrics Improved processing efficiency. Reduced memory utilization. Increased signal accuracy. Licensing & Attribution © 2024 Mupsje aka CasaTropical Professional Credits Original Ultimate and SuperSmoother concept: John F. Ehlers Maclaurin enhancement: Casa Tropical (CT) www.mathsisfun.com
Indicador Pine Script®
por Mupsje
4