DSL Trend Analysis [ChartPrime]The DSL Trend Analysis indicator utilizes Discontinued Signal Lines (DSL) deployed directly on price, combined with dynamic bands, to analyze the trend strength and momentum of price movements. By tracking the high and low price values and comparing them to the DSL bands, it provides a visual representation of trend momentum, highlighting both strong and weakening phases of market direction.
⯁ KEY FEATURES AND HOW TO USE
⯌ DSL-Based Trend Detection :
This indicator uses Discontinued Signal Lines (DSL) to evaluate price action. When the high stays above the upper DSL band, the line turns lime, indicating strong upward momentum. Similarly, when the low stays below the lower DSL band, the line turns orange, indicating strong downward momentum. Traders can use these visual signals to identify strong trends in either direction.
⯌ Bands for Trend Momentum :
The indicator plots dynamic bands around the DSL lines based on ATR (Average True Range). These bands provide a range within which price can fluctuate, helping to distinguish between strong and weakening trends. If the high remains within the upper band, the lime-colored line becomes transparent, showing weakening upward momentum. The same concept applies for the lower band, where the line turns orange with transparency, indicating weakening downward momentum.
If high and low stays between bands line has no color
to make sure indicator catches only strong momentum of price
⯌ Real-Time Band Price Labels :
The indicator places two labels on the chart, one at the upper DSL band and one at the lower DSL band, displaying the real-time price values of these bands. These labels help traders track the current price relative to the key bands, which are essential in determining potential breakout or reversal zones.
⯌ Visual Confirmation of Momentum Shifts :
By monitoring the relationship between the high and low values of the price relative to the DSL bands, this indicator provides a reliable way to confirm whether the trend is gaining or losing strength. This allows traders to act accordingly, whether it's to enter or exit positions based on trend strength or weakness.
⯁ USER INPUTS
Length : Defines the period used to calculate the DSL lines, influencing the sensitivity of the trend detection.
Offset : Adjusts the offset applied to the upper and lower DSL bands, affecting how the thresholds for strong or weak momentum are set.
Width (ATR Multiplier) : Determines the width of the DSL bands based on an ATR multiplier, providing a dynamic range around the price for momentum analysis.
⯁ CONCLUSION
The DSL Trend Analysis indicator is a powerful tool for assessing price momentum and trend strength. By combining Discontinued Signal Lines with dynamically calculated bands, traders can easily spot key moments when momentum shifts from strong to weak or vice versa. The color-coded lines and real-time price labels provide valuable insights for trading decisions in both trending and ranging markets.

# DSL

DSL Oscillator [BigBeluga]DSL Oscillator BigBeluga
The DSL (Discontinued Signal Lines) Oscillator is an advanced technical analysis tool that combines elements of the Relative Strength Index (RSI), Discontinued Signal Lines, and Zero-Lag Exponential Moving Average (ZLEMA). This versatile indicator is designed to help traders identify trend direction, momentum, and potential reversal points in the market.
What are Discontinued Signal Lines (DSL)?
Discontinued Signal Lines are an extension of the traditional signal line concept used in many indicators. While a standard signal line compares an indicator's value to its smoothed (slightly lagging) state, DSL takes this idea further by using multiple adaptive lines that respond to the indicator's current value. This approach provides a more nuanced view of the indicator's state and momentum, making it easier to determine trends and desired states of the indicator.
🔵 KEY FEATURES
● Discontinued Signal Lines (DSL)
Uses multiple adaptive lines that respond to the indicator's value
Provides a more nuanced view of the indicator's state and momentum
Helps determine trends and desired states of the indicator more effectively
Available in "Fast" and "Slow" modes for different responsiveness
Acts as dynamic support and resistance levels for the oscillator
● DSL Oscillator
Based on a combination of RSI and Discontinued Signal Lines
// Discontinued Signal Lines
dsl_lines(src, length)=>
UP = 0.
DN = 0.
UP := (src > ta.sma(src, length)) ? nz(UP ) + dsl_mode / length * (src - nz(UP )) : nz(UP )
DN := (src < ta.sma(src, length)) ? nz(DN ) + dsl_mode / length * (src - nz(DN )) : nz(DN )
Smoothed using Zero-Lag Exponential Moving Average for reduced lag
// Zero-Lag Exponential Moving Average function
zlema(src, length) =>
lag = math.floor((length - 1) / 2)
ema_data = 2 * src - src
ema2 = ta.ema(ema_data, length)
ema2
Oscillates between 0 and 100
Color-coded for easy interpretation of market conditions
● Signal Generation
Generates buy signals when the oscillator crosses above the lower DSL line below 50
Generates sell signals when the oscillator crosses below the upper DSL line above 50
Signals are visualized on both the oscillator and the main chart
● Visual Cues
Background color changes on signal occurrences for easy identification
Candles on the main chart are colored based on the latest signal
Oscillator line color changes based on its position relative to the DSL lines
🔵 HOW TO USE
● Trend Identification
Use the color and position of the DSL Oscillator relative to its Discontinued Signal Lines to determine the overall market trend
● Entry Signals
Look for buy signals (green circles) when the oscillator crosses above the lower DSL line
Look for sell signals (blue circles) when the oscillator crosses below the upper DSL line
Confirm signals with the triangles on the main chart and background color changes
● Exit Signals
Consider exiting long positions on exit signals and short positions on Entery signals
Watch for the oscillator crossing back between the DSL lines as a potential early exit signal
● Momentum Analysis
Strong momentum is indicated when the oscillator moves rapidly towards extremes and away from the DSL lines
Weakening momentum can be spotted when the oscillator struggles to reach new highs or lows, or starts converging with the DSL lines
The space between the DSL lines can indicate potential momentum strength - wider gaps suggest stronger trends
● Confirmation
Use the DSL lines as dynamic support/resistance levels for the oscillator
Look for convergence between oscillator signals and price action on the main chart
Combine signals with other technical indicators or chart patterns for stronger confirmation
🔵 CUSTOMIZATION
The DSL Oscillator offers several customization options:
Adjust the main calculation length for the DSL lines
Choose between "Fast" and "Slow" modes for the DSL lines calculation
By fine-tuning these settings, traders can adapt the DSL Oscillator to various market conditions and personal trading strategies.
The DSL Oscillator provides a multi-faceted approach to market analysis, combining trend identification, momentum assessment, and signal generation in one comprehensive tool. Its dynamic nature and visual cues make it suitable for both novice and experienced traders across various timeframes and markets. The integration of RSI, Discontinued Signal Lines, and ZLEMA offers traders a sophisticated yet intuitive tool to inform their trading decisions.
The use of Discontinued Signal Lines sets this oscillator apart from traditional indicators by providing a more adaptive and nuanced view of market conditions. This can potentially lead to more accurate trend identification and signal generation, especially in markets with varying volatility.
Traders can use the DSL Oscillator to identify trends, spot potential reversals, and gauge market momentum. The combination of the oscillator, dynamic signal lines, and clear visual signals provides a holistic view of market conditions. As with all technical indicators, it's recommended to use the DSL Oscillator in conjunction with other forms of analysis and within the context of a well-defined trading strategy.

Stochastic of Two-Pole SuperSmoother [Loxx]Stochastic of Two-Pole SuperSmoother is a Stochastic Indicator that takes as input Two-Pole SuperSmoother of price. Includes gradient coloring and Discontinued Signal Lines signals with alerts.
What is Ehlers ; Two-Pole Super Smoother?
From "Cycle Analytics for Traders Advanced Technical Trading Concepts" by John F. Ehlers
A SuperSmoother filter is used anytime a moving average of any type would otherwise be used, with the result that the SuperSmoother filter output would have substantially less lag for an equivalent amount of smoothing produced by the moving average. For example, a five-bar SMA has a cutoff period of approximately 10 bars and has two bars of lag. A SuperSmoother filter with a cutoff period of 10 bars has a lag a half bar larger than the two-pole modified Butterworth filter.Therefore, such a SuperSmoother filter has a maximum lag of approximately 1.5 bars and even less lag into the attenuation band of the filter. The differential in lag between moving average and SuperSmoother filter outputs becomes even larger when the cutoff periods are larger.
Market data contain noise, and removal of noise is the reason for using smoothing filters. In fact, market data contain several kinds of noise. I’ll group one kind of noise as systemic, caused by the random events of trades being exercised. A second kind of noise is aliasing noise, caused by the use of sampled data. Aliasing noise is the dominant term in the data for shorter cycle periods.
It is easy to think of market data as being a continuous waveform, but it is not. Using the closing price as representative for that bar constitutes one sample point. It doesn’t matter if you are using an average of the high and low instead of the close, you are still getting one sample per bar. Since sampled data is being used, there are some dSP aspects that must be considered. For example, the shortest analysis period that is possible (without aliasing)2 is a two-bar cycle.This is called the Nyquist frequency, 0.5 cycles per sample.A perfect two-bar sine wave cycle sampled at the peaks becomes a square wave due to sampling. However, sampling at the cycle peaks can- not be guaranteed, and the interference between the sampling frequency and the data frequency creates the aliasing noise.The noise is reduced as the data period is longer. For example, a four-bar cycle means there are four samples per cycle. Because there are more samples, the sampled data are a better replica of the sine wave component. The replica is better yet for an eight-bar data component.The improved fidelity of the sampled data means the aliasing noise is reduced at longer and longer cycle periods.The rate of reduction is 6 dB per octave. My experience is that the systemic noise rarely is more than 10 dB below the level of cyclic information, so that we create two conditions for effective smoothing of aliasing noise:
1. It is difficult to use cycle periods shorter that two octaves below the Nyquist frequency.That is, an eight-bar cycle component has a quantization noise level 12 dB below the noise level at the Nyquist frequency. longer cycle components therefore have a systemic noise level that exceeds the aliasing noise level.
2. A smoothing filter should have sufficient selectivity to reduce aliasing noise below the systemic noise level. Since aliasing noise increases at the rate of 6 dB per octave above a selected filter cutoff frequency and since the SuperSmoother attenuation rate is 12 dB per octave, the Super- Smoother filter is an effective tool to virtually eliminate aliasing noise in the output signal.
What are DSL Discontinued Signal Line?
A lot of indicators are using signal lines in order to determine the trend (or some desired state of the indicator) easier. The idea of the signal line is easy : comparing the value to it's smoothed (slightly lagging) state, the idea of current momentum/state is made.
Discontinued signal line is inheriting that simple signal line idea and it is extending it : instead of having one signal line, more lines depending on the current value of the indicator.
"Signal" line is calculated the following way :
When a certain level is crossed into the desired direction, the EMA of that value is calculated for the desired signal line
When that level is crossed into the opposite direction, the previous "signal" line value is simply "inherited" and it becomes a kind of a level
This way it becomes a combination of signal lines and levels that are trying to combine both the good from both methods.
In simple terms, DSL uses the concept of a signal line and betters it by inheriting the previous signal line's value & makes it a level.
Included:
Bar coloring
Alerts
Signals
Loxx's Expanded Source Types

Lyapunov Hodrick-Prescott Oscillator w/ DSL [Loxx]Lyapunov Hodrick-Prescott Oscillator w/ DSL is a Hodrick-Prescott Channel Filter that is modified using the Lyapunov stability algorithm to turn the filter into an oscillator. Signals are created using Discontinued Signal Lines.
What is the Lyapunov Stability?
As soon as scientists realized that the evolution of physical systems can be described in terms of mathematical equations, the stability of the various dynamical regimes was recognized as a matter of primary importance. The interest for this question was not only motivated by general curiosity, but also by the need to know, in the XIX century, to what extent the behavior of suitable mechanical devices remains unchanged, once their configuration has been perturbed. As a result, illustrious scientists such as Lagrange, Poisson, Maxwell and others deeply thought about ways of quantifying the stability both in general and specific contexts. The first exact definition of stability was given by the Russian mathematician Aleksandr Lyapunov who addressed the problem in his PhD Thesis in 1892, where he introduced two methods, the first of which is based on the linearization of the equations of motion and has originated what has later been termed Lyapunov exponents (LE). (Lyapunov 1992)
The interest in it suddenly skyrocketed during the Cold War period when the so-called "Second Method of Lyapunov" (see below) was found to be applicable to the stability of aerospace guidance systems which typically contain strong nonlinearities not treatable by other methods. A large number of publications appeared then and since in the control and systems literature. More recently the concept of the Lyapunov exponent (related to Lyapunov's First Method of discussing stability) has received wide interest in connection with chaos theory . Lyapunov stability methods have also been applied to finding equilibrium solutions in traffic assignment problems.
In practice, Lyapunov exponents can be computed by exploiting the natural tendency of an n-dimensional volume to align along the n most expanding subspace. From the expansion rate of an n-dimensional volume, one obtains the sum of the n largest Lyapunov exponents. Altogether, the procedure requires evolving n linearly independent perturbations and one is faced with the problem that all vectors tend to align along the same direction. However, as shown in the late '70s, this numerical instability can be counterbalanced by orthonormalizing the vectors with the help of the Gram-Schmidt procedure (Benettin et al. 1980, Shimada and Nagashima 1979) (or, equivalently with a QR decomposition). As a result, the LE λi, naturally ordered from the largest to the most negative one, can be computed: they are altogether referred to as the Lyapunov spectrum.
The Lyapunov exponent "λ" , is useful for distinguishing among the various types of orbits. It works for discrete as well as continuous systems.
λ < 0
The orbit attracts to a stable fixed point or stable periodic orbit. Negative Lyapunov exponents are characteristic of dissipative or non-conservative systems (the damped harmonic oscillator for instance). Such systems exhibit asymptotic stability; the more negative the exponent, the greater the stability. Superstable fixed points and superstable periodic points have a Lyapunov exponent of λ = −∞. This is something akin to a critically damped oscillator in that the system heads towards its equilibrium point as quickly as possible.
λ = 0
The orbit is a neutral fixed point (or an eventually fixed point). A Lyapunov exponent of zero indicates that the system is in some sort of steady state mode. A physical system with this exponent is conservative. Such systems exhibit Lyapunov stability. Take the case of two identical simple harmonic oscillators with different amplitudes. Because the frequency is independent of the amplitude, a phase portrait of the two oscillators would be a pair of concentric circles. The orbits in this situation would maintain a constant separation, like two flecks of dust fixed in place on a rotating record.
λ > 0
The orbit is unstable and chaotic. Nearby points, no matter how close, will diverge to any arbitrary separation. All neighborhoods in the phase space will eventually be visited. These points are said to be unstable. For a discrete system, the orbits will look like snow on a television set. This does not preclude any organization as a pattern may emerge. Thus the snow may be a bit lumpy. For a continuous system, the phase space would be a tangled sea of wavy lines like a pot of spaghetti. A physical example can be found in Brownian motion. Although the system is deterministic, there is no order to the orbit that ensues.
For our purposes here, we transform the HP by applying Lyapunov Stability as follows:
output = math.log(math.abs(HP / HP ))
You can read more about Lyapunov Stability here: Measuring Chaos
What is. the Hodrick-Prescott Filter?
The Hodrick-Prescott (HP) filter refers to a data-smoothing technique. The HP filter is commonly applied during analysis to remove short-term fluctuations associated with the business cycle. Removal of these short-term fluctuations reveals long-term trends.
The Hodrick-Prescott (HP) filter is a tool commonly used in macroeconomics. It is named after economists Robert Hodrick and Edward Prescott who first popularized this filter in economics in the 1990s. Hodrick was an economist who specialized in international finance. Prescott won the Nobel Memorial Prize, sharing it with another economist for their research in macroeconomics.
This filter determines the long-term trend of a time series by discounting the importance of short-term price fluctuations. In practice, the filter is used to smooth and detrend the Conference Board's Help Wanted Index (HWI) so it can be benchmarked against the Bureau of Labor Statistic's (BLS) JOLTS, an economic data series that may more accurately measure job vacancies in the U.S.
The HP filter is one of the most widely used tools in macroeconomic analysis. It tends to have favorable results if the noise is distributed normally, and when the analysis being conducted is historical.
What are DSL Discontinued Signal Line?
A lot of indicators are using signal lines in order to determine the trend (or some desired state of the indicator) easier. The idea of the signal line is easy : comparing the value to it's smoothed (slightly lagging) state, the idea of current momentum/state is made.
Discontinued signal line is inheriting that simple signal line idea and it is extending it : instead of having one signal line, more lines depending on the current value of the indicator.
"Signal" line is calculated the following way :
When a certain level is crossed into the desired direction, the EMA of that value is calculated for the desired signal line
When that level is crossed into the opposite direction, the previous "signal" line value is simply "inherited" and it becomes a kind of a level
This way it becomes a combination of signal lines and levels that are trying to combine both the good from both methods.
In simple terms, DSL uses the concept of a signal line and betters it by inheriting the previous signal line's value & makes it a level.
Included:
Bar coloring
Alerts
Signals
Loxx's Expanded Source Types

Smoother Moving Average w/ DSL [Loxx]Smoother Moving Average w/ DSL is a Smoother Filter indicator with Discontinued Signal Lines to drastically reduce noise and improve signal quality.
What is the Smoother Filter?
The Smoother filter is a faster-reacting smoothing technique which generates considerably less lag than the SMMA ( Smoothed Moving Average ). It gives earlier signals but can also create false signals due to its earlier reactions. This filter is sometimes wrongly mistaken for the superior Jurik Smoothing algorithm.
What are DSL Discontinued Signal Line?
A lot of indicators are using signal lines in order to determine the trend (or some desired state of the indicator) easier. The idea of the signal line is easy : comparing the value to it's smoothed (slightly lagging) state, the idea of current momentum/state is made.
Discontinued signal line is inheriting that simple signal line idea and it is extending it : instead of having one signal line, more lines depending on the current value of the indicator.
"Signal" line is calculated the following way :
When a certain level is crossed into the desired direction, the EMA of that value is calculated for the desired signal line
When that level is crossed into the opposite direction, the previous "signal" line value is simply "inherited" and it becomes a kind of a level
This way it becomes a combination of signal lines and levels that are trying to combine both the good from both methods.
In simple terms, DSL uses the concept of a signal line and betters it by inheriting the previous signal line's value & makes it a level.
Included
2 Signal types
Alerts
Loxx's Expanded Source Types
Bar coloring

Deviation Scaled Moving Average w/ DSL [Loxx]Deviation Scaled Moving Average w/ DSL as described in the “The Deviation-Scaled Moving Average.” article of July 2018 TASC . This is an adaptive moving average average that has the ability to rapidly adapt to volatility in price movement. This version adds Discontinued Signal Lines create the buy/sell signals.
What are DSL Discontinued Signal Line?
A lot of indicators are using signal lines in order to determine the trend (or some desired state of the indicator) easier. The idea of the signal line is easy : comparing the value to it's smoothed (slightly lagging) state, the idea of current momentum/state is made.
Discontinued signal line is inheriting that simple signal line idea and it is extending it : instead of having one signal line, more lines depending on the current value of the indicator.
"Signal" line is calculated the following way :
When a certain level is crossed into the desired direction, the EMA of that value is calculated for the desired signal line
When that level is crossed into the opposite direction, the previous "signal" line value is simply "inherited" and it becomes a kind of a level
This way it becomes a combination of signal lines and levels that are trying to combine both the good from both methods.
In simple terms, DSL uses the concept of a signal line and betters it by inheriting the previous signal line's value & makes it a level.
Included
2 Signal types
Alerts
Loxx's Expanded Source Types
Bar coloring

T3 Volatility Quality Index (VQI) w/ DSL & Pips Filtering [Loxx]T3 Volatility Quality Index (VQI) w/ DSL & Pips Filtering is a VQI indicator that uses T3 smoothing and discontinued signal lines to determine breakouts and breakdowns. This also allows filtering by pips.***
What is the Volatility Quality Index ( VQI )?
The idea behind the volatility quality index is to point out the difference between bad and good volatility in order to identify better trade opportunities in the market. This forex indicator works using the True Range algorithm in combination with the open, close, high and low prices.
What are DSL Discontinued Signal Line?
A lot of indicators are using signal lines in order to determine the trend (or some desired state of the indicator) easier. The idea of the signal line is easy : comparing the value to it's smoothed (slightly lagging) state, the idea of current momentum/state is made.
Discontinued signal line is inheriting that simple signal line idea and it is extending it : instead of having one signal line, more lines depending on the current value of the indicator.
"Signal" line is calculated the following way :
When a certain level is crossed into the desired direction, the EMA of that value is calculated for the desired signal line
When that level is crossed into the opposite direction, the previous "signal" line value is simply "inherited" and it becomes a kind of a level
This way it becomes a combination of signal lines and levels that are trying to combine both the good from both methods.
In simple terms, DSL uses the concept of a signal line and betters it by inheriting the previous signal line's value & makes it a level.
What is the T3 moving average?
Better Moving Averages Tim Tillson
November 1, 1998
Tim Tillson is a software project manager at Hewlett-Packard, with degrees in Mathematics and Computer Science. He has privately traded options and equities for 15 years.
Introduction
"Digital filtering includes the process of smoothing, predicting, differentiating, integrating, separation of signals, and removal of noise from a signal. Thus many people who do such things are actually using digital filters without realizing that they are; being unacquainted with the theory, they neither understand what they have done nor the possibilities of what they might have done."
This quote from R. W. Hamming applies to the vast majority of indicators in technical analysis . Moving averages, be they simple, weighted, or exponential, are lowpass filters; low frequency components in the signal pass through with little attenuation, while high frequencies are severely reduced.
"Oscillator" type indicators (such as MACD , Momentum, Relative Strength Index ) are another type of digital filter called a differentiator.
Tushar Chande has observed that many popular oscillators are highly correlated, which is sensible because they are trying to measure the rate of change of the underlying time series, i.e., are trying to be the first and second derivatives we all learned about in Calculus.
We use moving averages (lowpass filters) in technical analysis to remove the random noise from a time series, to discern the underlying trend or to determine prices at which we will take action. A perfect moving average would have two attributes:
It would be smooth, not sensitive to random noise in the underlying time series. Another way of saying this is that its derivative would not spuriously alternate between positive and negative values.
It would not lag behind the time series it is computed from. Lag, of course, produces late buy or sell signals that kill profits.
The only way one can compute a perfect moving average is to have knowledge of the future, and if we had that, we would buy one lottery ticket a week rather than trade!
Having said this, we can still improve on the conventional simple, weighted, or exponential moving averages. Here's how:
Two Interesting Moving Averages
We will examine two benchmark moving averages based on Linear Regression analysis.
In both cases, a Linear Regression line of length n is fitted to price data.
I call the first moving average ILRS, which stands for Integral of Linear Regression Slope. One simply integrates the slope of a linear regression line as it is successively fitted in a moving window of length n across the data, with the constant of integration being a simple moving average of the first n points. Put another way, the derivative of ILRS is the linear regression slope. Note that ILRS is not the same as a SMA ( simple moving average ) of length n, which is actually the midpoint of the linear regression line as it moves across the data.
We can measure the lag of moving averages with respect to a linear trend by computing how they behave when the input is a line with unit slope. Both SMA (n) and ILRS(n) have lag of n/2, but ILRS is much smoother than SMA .
Our second benchmark moving average is well known, called EPMA or End Point Moving Average. It is the endpoint of the linear regression line of length n as it is fitted across the data. EPMA hugs the data more closely than a simple or exponential moving average of the same length. The price we pay for this is that it is much noisier (less smooth) than ILRS, and it also has the annoying property that it overshoots the data when linear trends are present.
However, EPMA has a lag of 0 with respect to linear input! This makes sense because a linear regression line will fit linear input perfectly, and the endpoint of the LR line will be on the input line.
These two moving averages frame the tradeoffs that we are facing. On one extreme we have ILRS, which is very smooth and has considerable phase lag. EPMA has 0 phase lag, but is too noisy and overshoots. We would like to construct a better moving average which is as smooth as ILRS, but runs closer to where EPMA lies, without the overshoot.
A easy way to attempt this is to split the difference, i.e. use (ILRS(n)+EPMA(n))/2. This will give us a moving average (call it IE /2) which runs in between the two, has phase lag of n/4 but still inherits considerable noise from EPMA. IE /2 is inspirational, however. Can we build something that is comparable, but smoother? Figure 1 shows ILRS, EPMA, and IE /2.
Filter Techniques
Any thoughtful student of filter theory (or resolute experimenter) will have noticed that you can improve the smoothness of a filter by running it through itself multiple times, at the cost of increasing phase lag.
There is a complementary technique (called twicing by J.W. Tukey) which can be used to improve phase lag. If L stands for the operation of running data through a low pass filter, then twicing can be described by:
L' = L(time series) + L(time series - L(time series))
That is, we add a moving average of the difference between the input and the moving average to the moving average. This is algebraically equivalent to:
2L-L(L)
This is the Double Exponential Moving Average or DEMA , popularized by Patrick Mulloy in TASAC (January/February 1994).
In our taxonomy, DEMA has some phase lag (although it exponentially approaches 0) and is somewhat noisy, comparable to IE /2 indicator.
We will use these two techniques to construct our better moving average, after we explore the first one a little more closely.
Fixing Overshoot
An n-day EMA has smoothing constant alpha=2/(n+1) and a lag of (n-1)/2.
Thus EMA (3) has lag 1, and EMA (11) has lag 5. Figure 2 shows that, if I am willing to incur 5 days of lag, I get a smoother moving average if I run EMA (3) through itself 5 times than if I just take EMA (11) once.
This suggests that if EPMA and DEMA have 0 or low lag, why not run fast versions (eg DEMA (3)) through themselves many times to achieve a smooth result? The problem is that multiple runs though these filters increase their tendency to overshoot the data, giving an unusable result. This is because the amplitude response of DEMA and EPMA is greater than 1 at certain frequencies, giving a gain of much greater than 1 at these frequencies when run though themselves multiple times. Figure 3 shows DEMA (7) and EPMA(7) run through themselves 3 times. DEMA^3 has serious overshoot, and EPMA^3 is terrible.
The solution to the overshoot problem is to recall what we are doing with twicing:
DEMA (n) = EMA (n) + EMA (time series - EMA (n))
The second term is adding, in effect, a smooth version of the derivative to the EMA to achieve DEMA . The derivative term determines how hot the moving average's response to linear trends will be. We need to simply turn down the volume to achieve our basic building block:
EMA (n) + EMA (time series - EMA (n))*.7;
This is algebraically the same as:
EMA (n)*1.7-EMA( EMA (n))*.7;
I have chosen .7 as my volume factor, but the general formula (which I call "Generalized Dema") is:
GD (n,v) = EMA (n)*(1+v)-EMA( EMA (n))*v,
Where v ranges between 0 and 1. When v=0, GD is just an EMA , and when v=1, GD is DEMA . In between, GD is a cooler DEMA . By using a value for v less than 1 (I like .7), we cure the multiple DEMA overshoot problem, at the cost of accepting some additional phase delay. Now we can run GD through itself multiple times to define a new, smoother moving average T3 that does not overshoot the data:
T3(n) = GD ( GD ( GD (n)))
In filter theory parlance, T3 is a six-pole non-linear Kalman filter. Kalman filters are ones which use the error (in this case (time series - EMA (n)) to correct themselves. In Technical Analysis , these are called Adaptive Moving Averages; they track the time series more aggressively when it is making large moves.
Included
Signals
Alerts
Related indicators
Zero-line Volatility Quality Index (VQI)
Volatility Quality Index w/ Pips Filtering
Variety Moving Average Waddah Attar Explosion (WAE)
***This indicator is tuned to Forex. If you want to make it useful for other tickers, you must change the pip filtering value to match the asset. This means that for BTC, for example, you likely need to use a value of 10,000 or more for pips filter.

Synthetic EMA Momentum w/ DSL [Loxx]Synthetic EMA Momentum w/ DSL is a momentum indicator that is calculated with 5 different EMAs of increasing period to derive a final momentum value. This helps reduce noise and improve signal quality. Discontinued signal lines are uses to calculate signal values.
What are DSL Discontinued Signal Line?
A lot of indicators are using signal lines in order to determine the trend (or some desired state of the indicator) easier. The idea of the signal line is easy : comparing the value to it's smoothed (slightly lagging) state, the idea of current momentum/state is made.
Discontinued signal line is inheriting that simple signal line idea and it is extending it : instead of having one signal line, more lines depending on the current value of the indicator.
"Signal" line is calculated the following way :
When a certain level is crossed into the desired direction, the EMA of that value is calculated for the desired signal line
When that level is crossed into the opposite direction, the previous "signal" line value is simply "inherited" and it becomes a kind of a level
This way it becomes a combination of signal lines and levels that are trying to combine both the good from both methods.
In simple terms, DSL uses the concept of a signal line and betters it by inheriting the previous signal line's value & makes it a level.
Included:
Loxx's Expanded Source Types
Alerts
Signals
Bar coloring
Related indicators
Smoother Momentum MACD w/ DSL
T3 Velocity

STD-Filtered Variety RSI of Double Averages w/ DSL [Loxx]STD-Filtered Variety RSI of Double Averages w/ DSL is a standard deviation step filtered RSI indicator that is calculated using double smoothing. The user can choose from 8 different RSI types and 38 different double smoothing types. This indicator uses Discontinued Signal Lines instead of regular signals and levels. This allows the signals to be more precise in catching early trend breakouts and breakdowns.
Things to note
Double smoothing of the source does not function like DEMA, for example. This double smoothing is just smoothing of smoothing of source
There are two types of smoothing for Discontinued Signals Lines: Regular EMA and Fast EMA
T3 RSI has been added on top of Loxx's Variety RSI library
Contained inside this indicator
Loxx's Moving Averages
Loxx's Variety RSI
Related indicators
Corrected RSI w/ Floating Levels
Adaptive, Jurik-Filtered, Floating RSI
Variety RSI w/ Dynamic Zones
Included
Bar coloring
Alerts
2 types of signals with precision adjustment
Loxx's Variety RSI
Loxx's Moving Averages

R-squared Adaptive T3 w/ DSL [Loxx]R-squared Adaptive T3 w/ DSL is the following T3 indicator but with Discontinued Signal Lines added to reduce noise and thereby increase signal accuracy. This adaptation makes this indicator lower TF scalp friendly.
What is R-squared Adaptive?
One tool available in forecasting the trendiness of the breakout is the coefficient of determination ( R-squared ), a statistical measurement.
The R-squared indicates linear strength between the security's price (the Y - axis) and time (the X - axis). The R-squared is the percentage of squared error that the linear regression can eliminate if it were used as the predictor instead of the mean value. If the R-squared were 0.99, then the linear regression would eliminate 99% of the error for prediction versus predicting closing prices using a simple moving average .
R-squared is used here to derive a T3 factor used to modify price before passing price through a six-pole non-linear Kalman filter.
What is the T3 moving average?
Better Moving Averages Tim Tillson
November 1, 1998
Tim Tillson is a software project manager at Hewlett-Packard, with degrees in Mathematics and Computer Science. He has privately traded options and equities for 15 years.
Introduction
"Digital filtering includes the process of smoothing, predicting, differentiating, integrating, separation of signals, and removal of noise from a signal. Thus many people who do such things are actually using digital filters without realizing that they are; being unacquainted with the theory, they neither understand what they have done nor the possibilities of what they might have done."
This quote from R. W. Hamming applies to the vast majority of indicators in technical analysis . Moving averages, be they simple, weighted, or exponential, are lowpass filters; low frequency components in the signal pass through with little attenuation, while high frequencies are severely reduced.
"Oscillator" type indicators (such as MACD , Momentum, Relative Strength Index ) are another type of digital filter called a differentiator.
Tushar Chande has observed that many popular oscillators are highly correlated, which is sensible because they are trying to measure the rate of change of the underlying time series, i.e., are trying to be the first and second derivatives we all learned about in Calculus.
We use moving averages (lowpass filters) in technical analysis to remove the random noise from a time series, to discern the underlying trend or to determine prices at which we will take action. A perfect moving average would have two attributes:
It would be smooth, not sensitive to random noise in the underlying time series. Another way of saying this is that its derivative would not spuriously alternate between positive and negative values.
It would not lag behind the time series it is computed from. Lag, of course, produces late buy or sell signals that kill profits.
The only way one can compute a perfect moving average is to have knowledge of the future, and if we had that, we would buy one lottery ticket a week rather than trade!
Having said this, we can still improve on the conventional simple, weighted, or exponential moving averages. Here's how:
Two Interesting Moving Averages
We will examine two benchmark moving averages based on Linear Regression analysis.
In both cases, a Linear Regression line of length n is fitted to price data.
I call the first moving average ILRS, which stands for Integral of Linear Regression Slope. One simply integrates the slope of a linear regression line as it is successively fitted in a moving window of length n across the data, with the constant of integration being a simple moving average of the first n points. Put another way, the derivative of ILRS is the linear regression slope. Note that ILRS is not the same as a SMA ( simple moving average ) of length n, which is actually the midpoint of the linear regression line as it moves across the data.
We can measure the lag of moving averages with respect to a linear trend by computing how they behave when the input is a line with unit slope. Both SMA (n) and ILRS(n) have lag of n/2, but ILRS is much smoother than SMA .
Our second benchmark moving average is well known, called EPMA or End Point Moving Average. It is the endpoint of the linear regression line of length n as it is fitted across the data. EPMA hugs the data more closely than a simple or exponential moving average of the same length. The price we pay for this is that it is much noisier (less smooth) than ILRS, and it also has the annoying property that it overshoots the data when linear trends are present.
However, EPMA has a lag of 0 with respect to linear input! This makes sense because a linear regression line will fit linear input perfectly, and the endpoint of the LR line will be on the input line.
These two moving averages frame the tradeoffs that we are facing. On one extreme we have ILRS, which is very smooth and has considerable phase lag. EPMA has 0 phase lag, but is too noisy and overshoots. We would like to construct a better moving average which is as smooth as ILRS, but runs closer to where EPMA lies, without the overshoot.
A easy way to attempt this is to split the difference, i.e. use (ILRS(n)+EPMA(n))/2. This will give us a moving average (call it IE /2) which runs in between the two, has phase lag of n/4 but still inherits considerable noise from EPMA. IE /2 is inspirational, however. Can we build something that is comparable, but smoother? Figure 1 shows ILRS, EPMA, and IE /2.
Filter Techniques
Any thoughtful student of filter theory (or resolute experimenter) will have noticed that you can improve the smoothness of a filter by running it through itself multiple times, at the cost of increasing phase lag.
There is a complementary technique (called twicing by J.W. Tukey) which can be used to improve phase lag. If L stands for the operation of running data through a low pass filter, then twicing can be described by:
L' = L(time series) + L(time series - L(time series))
That is, we add a moving average of the difference between the input and the moving average to the moving average. This is algebraically equivalent to:
2L-L(L)
This is the Double Exponential Moving Average or DEMA , popularized by Patrick Mulloy in TASAC (January/February 1994).
In our taxonomy, DEMA has some phase lag (although it exponentially approaches 0) and is somewhat noisy, comparable to IE /2 indicator.
We will use these two techniques to construct our better moving average, after we explore the first one a little more closely.
Fixing Overshoot
An n-day EMA has smoothing constant alpha=2/(n+1) and a lag of (n-1)/2.
Thus EMA (3) has lag 1, and EMA (11) has lag 5. Figure 2 shows that, if I am willing to incur 5 days of lag, I get a smoother moving average if I run EMA (3) through itself 5 times than if I just take EMA (11) once.
This suggests that if EPMA and DEMA have 0 or low lag, why not run fast versions (eg DEMA (3)) through themselves many times to achieve a smooth result? The problem is that multiple runs though these filters increase their tendency to overshoot the data, giving an unusable result. This is because the amplitude response of DEMA and EPMA is greater than 1 at certain frequencies, giving a gain of much greater than 1 at these frequencies when run though themselves multiple times. Figure 3 shows DEMA (7) and EPMA(7) run through themselves 3 times. DEMA^3 has serious overshoot, and EPMA^3 is terrible.
The solution to the overshoot problem is to recall what we are doing with twicing:
DEMA (n) = EMA (n) + EMA (time series - EMA (n))
The second term is adding, in effect, a smooth version of the derivative to the EMA to achieve DEMA . The derivative term determines how hot the moving average's response to linear trends will be. We need to simply turn down the volume to achieve our basic building block:
EMA (n) + EMA (time series - EMA (n))*.7;
This is algebraically the same as:
EMA (n)*1.7-EMA( EMA (n))*.7;
I have chosen .7 as my volume factor, but the general formula (which I call "Generalized Dema") is:
GD (n,v) = EMA (n)*(1+v)-EMA( EMA (n))*v,
Where v ranges between 0 and 1. When v=0, GD is just an EMA , and when v=1, GD is DEMA . In between, GD is a cooler DEMA . By using a value for v less than 1 (I like .7), we cure the multiple DEMA overshoot problem, at the cost of accepting some additional phase delay. Now we can run GD through itself multiple times to define a new, smoother moving average T3 that does not overshoot the data:
T3(n) = GD ( GD ( GD (n)))
In filter theory parlance, T3 is a six-pole non-linear Kalman filter. Kalman filters are ones which use the error (in this case (time series - EMA (n)) to correct themselves. In Technical Analysis , these are called Adaptive Moving Averages; they track the time series more aggressively when it is making large moves.
Included:
Bar coloring
Signals
Alerts
EMA and FEMA Signla/DSL smoothing
Loxx's Expanded Source Types

PPO w/ Discontinued Signal Lines [Loxx]PPO w/ Discontinued Signal Lines is a Percentage Price Oscillator with some upgrades. This indicator has 33 source types and 35+ moving average types as well as Discontinued Signal Lines and divergences. These additions reduce noise and increase hit rate.
What is the Price Percentage Oscillator?
The percentage price oscillator (PPO) is a technical momentum indicator that shows the relationship between two moving averages in percentage terms. The moving averages are a 26-period and 12-period exponential moving average (EMA).
The PPO is used to compare asset performance and volatility, spot divergence that could lead to price reversals, generate trade signals, and help confirm trend direction.
Included:
Bar coloring
3 signal variations w/ alerts
Divergences w/ alerts
Loxx's Expanded Source Types
Loxx's Moving Averages

VIDYA DMI Oscillator w/ DSL Levels [Loxx]VIDYA DMI Oscillator w/ DSL Levels is a VIDYA smoothed Direction Movement Index with Discontinued Signals. These two add on features allow for more accurate signals by reducing noise.
What is the Direction Movement Index?
Within the suite of indicators that make up Wilder’s directional movement index (DMI) are the plus directional movement indicator (+DI) and the minus directional movement indicator (-DI). They provide the foundation for the more widely recognized average directional index (ADX). Whereas the ADX offers information about the strength of price movement but not its direction, the +DI and -DI furnish information about the positive or negative direction of price movement over a period of time.
Wilder provides complete information about the function and construction of all the components that make up the directional movement index in his 1978 book, New Concepts In Technical Trading Systems. In general, the plus and minus components of the DMI focus on that portion of the current bar’s trading range that is outside the range of the previous price bar. If it is higher, it is considered to be positive (+) and if it is lower, it is labeled negative (-). These values are divided by the true range and averaged over time, usually 14 periods. A move by the +DI above the -DI indicates that positive or upward price direction has overtaken negative or downward price direction. Conversely, when +DI falls below -DI, declining price either from selling pressure or lack of upward price momentum is taking control. Potential changes in direction or trend occur when the lines intersect.
What is VIDYA?
VIDYA (Chande's Variable Index Dynamic Average) is an adaptive weighted moving average indicator. It was developed by Tushar Chande as an attempt to improve the performance of the EMA (Exponential Weighted Moving Average) indicator.
Included:
Bar coloring
3 signal variations w/ alerts
4 intermediate smoothing types
Loxx's Expanded Source Types

RSI/RSX QQE Histogram w/ Discontinued Signal Line [Loxx]QQE Histogram w/ Discontinued Signal Line is a run-of-the-mill Qualitative Quantitative Estimation (QQE) calculation but with a signal line to better filter and identify trends. The thicker white line is the QSL and appears as a simple EMA. The two thin white lines are the fast and slow trends. The histogram changes color based on the DSL levels. This version of QQE also includes two different versions of RSI: Wilders and Jurik's RSX.
What is Qualitative Quantitative Estimation (QQE)?
The Qualitative Quantitative Estimation (QQE) indicator works like a smoother version of the popular Relative Strength Index ( RSI ) indicator. QQE expands on RSI by adding two volatility based trailing stop lines. These trailing stop lines are composed of a fast and a slow moving Average True Range (ATR).
What is Wilders' RSI?
The Relative Strength Index (RSI) is a well versed momentum based oscillator which is used to measure the speed (velocity) as well as the change (magnitude) of directional price movements. Essentially RSI , when graphed, provides a visual mean to monitor both the current, as well as historical, strength and weakness of a particular market. The strength or weakness is based on closing prices over the duration of a specified trading period creating a reliable metric of price and momentum changes. Given the popularity of cash settled instruments (stock indexes) and leveraged financial products (the entire field of derivatives); RSI has proven to be a viable indicator of price movements.
What is RSX?
RSI is a very popular technical indicator, because it takes into consideration market speed, direction and trend uniformity. However, the its widely criticized drawback is its noisy (jittery) appearance. The Jurk RSX retains all the useful features of RSI , but with one important exception: the noise is gone with no added lag.
There are many indicators for many purposes. Some of them are complex and some are comparatively easy to handle. The QQE indicator is a really useful analytical tool and one of the most accurate indicators. It offers numerous strategies for using the buy and sell signals. Essentially, it can help detect trend reversal and enter the trade at the most optimal positions.
Included:
-Toggle on/off bar coloring

Trend Trigger Factor w/ Discontinued Signal Lines [Loxx]Trend Trigger Factor w/ Discontinued Signal Lines is a Trend Trigger Factor indicator with floating boundary lines to identify trends earlier
What is the Trend Trigger Factor?
Designed by M.H. Pee, the Trend Trigger Factors role is to help traders detect uptrends and downtrends and thus allow them to better position themselves in a with-trend manner. Its creator argues that the markets are mostly random but have a small trend component, which is the most crucial part of trading success. Being able to determine whether the market is in a bull or bear trend and how strong that trend is will allow you to be on the right side of the market for longer, capitalizing as much as possible on its trending behavior.
In his article, M.H. Pee used a 15-period trackback span to explain the calculations. The TTF formula is based on the so-called Buy Power and Sell Power. In his example, Pee labeled today as day 1, yesterday as day 2, the preceding day as day 3 and so on
What's new in this indicator?
Averages filter out prices prior to being used in calculation. That way the lag added is smaller than when the smoothing is used on the calculated result.
Unlike the original which uses levels +100 and -100 as significant levels for signal triggering, this version is using discontinued signal lines for trend filtering. That way it makes it a bit more responsive to market conditions
How do I use this?
The Trend Trigger Factor is similar in interpretation to the Relative Strength Index. It is plotted on a scale with most prominent levels at +100 and -100, crosses of which logically signal possible trade entries. The difference here, however, is that the upper and lower boundary flex with price movements so the upper and lower boundary shift dynamically. Crosses above the top line signify bullish sentiment, crossed below the the bottom line signify bearish sentiment.