Fair value bands / quantifytools— Overview
Fair value bands, like other band tools, depict dynamic points in price where price behaviour is normal or abnormal, i.e. trading at/around mean (price at fair value) or deviating from mean (price outside fair value). Unlike constantly readjusting standard deviation based bands, fair value bands are designed to be smooth and constant, based on typical historical deviations. The script calculates pivots that take place above/below fair value basis and forms median deviation bands based on this information. These points are then multiplied up to 3, representing more extreme deviations.
By default, the script uses OHLC4 and SMA 20 as basis for the bands. Users can form their preferred fair value basis using following options:
Price source
- Standard OHLC values
- HL2 (High + low / 2)
- OHLC4 (Open + high + low + close / 4)
- HLC3 (High + low + close / 3)
- HLCC4 (High + low + close + close / 4)
Smoothing
- SMA
- EMA
- HMA
- RMA
- WMA
- VWMA
- Median
Once fair value basis is established, some additional customization options can be employed:
Trend mode
Direction based
Cross based
Trend modes affect fair value basis color that indicates trend direction. Direction based trend considers only the direction of the defined fair value basis, i.e. pointing up is considered an uptrend, vice versa for downtrend. Cross based trends activate when selected source (same options as price source) crosses fair value basis. These sources can be set individually for uptrend/downtrend cross conditions. By default, the script uses cross based trend mode with low and high as sources.
Cross based (downtrend not triggered) vs. direction based (downtrend triggered):
Threshold band
Threshold band is calculated using typical deviations when price is trading at fair value basis. In other words, a little bit of "wiggle room" is added around the mean based on expected deviation. This feature is useful for cross based trends, as it allows filtering insignificant crosses that are more likely just noise. By default, threshold band is calculated based on 1x median deviation from mean. Users can increase/decrease threshold band width via input menu for more/less noise filtering, e.g. 2x threshold band width would require price to cross wiggle room that is 2x wider than typical, 0x erases threshold band altogether.
Deviation bands
Width of deviation bands by default is based on 1x median deviations and can be increased/decreased in a similar manner to threshold bands.
Each combination of customization options produces varying behaviour in the bands. To measure the behaviour and finding fairest representation of fair and unfair value, some data is gathered.
— Fair value metrics
Space between each band is considered a lot, named +3, +2, +1, -1, -2, -3. For each lot, time spent and volume relative to volume moving average (SMA 20) is recorded each time price is trading in a given lot:
Depending on the asset, timeframe and chosen fair value basis, shape of the distributions vary. However, practically always time is distributed in a normal bell curve shape, being highest at lots +1 to -1, gradually decreasing the further price is from the mean. This is hardly surprising, but it allows accurately determining dynamic areas of normal and abnormal price behaviour (i.e. low risk area between +1 and -1, high risk area between +-2 to +-3). Volume on the other hand is typically distributed the other way around, being lowest at lots +1 to -1 and highest at +-2 to +-3. When time and volume are distributed like so, we can conclude that 1) price being outside fair value is a rare event and 2) the more price is outside fair value, the more anomaly behaviour in volume we tend to find.
Viewing metric calculations
Metric calculation highlights can be enabled from the input menu, resulting in a lot based coloring and visibility of each lot counter (time, cumulative relative volume and average relative volume) in data window:
— Alerts
Available alerts are the following:
Individual
- High crossing deviation band (bands +1 to +3 )
- Low crossing deviation band (bands -1 to -3 )
- Low at threshold band in an uptrend
- High at threshold band in a downtrend
- New uptrend
- New downtrend
Grouped
- New uptrend or downtrend
- Deviation band cross (+1 or -1)
- Deviation band cross (+2 or -2)
- Deviation band cross (+3 or -3)
— Practical guide
Example #1 : Risk on/risk off trend following
Ideal trend stays inside fair value and provides sufficient cool offs between the moves. When this is the case, fair value bands can be used for sensible entry/exit levels within the trend.
Example #2 : Mean reversions
When price shows exuberance into an extreme deviation, followed by a stall and signs of exhaustion (wicks), an opportunity for mean reversion emerges. The higher the deviation, the more volatility in the move, the more signalling of exhaustion, the better.
Example #3 : Tweaking bands for desired behaviour
The faster the length of fair value basis, the more momentum price needs to hit extreme deviation levels, as bands too are moving faster alongside price. Decreasing fair value basis length typically leads to more quick and aggressive deviations and less steady trends outside fair value.
Desvio Padrão
GAVAD - Selling after a Strong MovimentThis strategy search for a moment whe the market make two candles are consistently strong, and open a Sell, searching the imediactly correction, on the new candle. It`s easy to see the bars on the histogram graph. Purple Bars represent the candle variation. when on candle cross ove the Signal line the graph plot an Yellow ci, if the second bar crossover the signal a green circle is ploted and the operation start on start of the next candle.
This strategy can be used in a lot of Stocks and other graphs. many times we need a small time of graph, maybe 1 or 5 minutes because the gain shoud be planned to a midle of the second candle. You need look the stocks you will use.
Stocks > 100 dolars isnt great, markets extremly volatly not too. but, Stocks that have a consistently development are very interisting. Look to markets searching maybe 0.5% or 1%.
For this moment, I make the development of a Brasilian Real x American Dollar. In 15 Minutes.
if you use in small timeframe the results can be better.
On this time we make more than 500 trades with a small lot of contracts, without a big percent profitable, but a small profit in each operation, maybe you search more than. To present a real trading system I insert a spreed to present a correct view of the results.
Each stock, Index, or crypto there is a specific configuration?
my suggestion for new stocks
You need choice a stock and using the setup search set over than 70% gain (percent profitable), using a 1% of gain and loss between 1-2%
as the exemple (WDO)
default I prepare a Brazilian Index
6-signal (6% is variation of a candle of the last candle)
10000- multiplicator (its important to configure diferences betwen a stock and an Indice)
gain 3 (this proportion will be set looking you target, how I say, 1% can be good)
loss 8 (this proportion will be set with you bankroll management, how I say, maybe 2%, you need evaluate)
for maximize operations I use in the 1 or 5 minute graph. Timeframes more large make slowlly results,
(but not unable that you use in a 1 hour or a 1 day.)
I make this script by zero. Maybe the code doesnt so organized, but is very easy to understand. If you have any doubts . leave a comment.
I hope help you.
Up Down VolatilityThis is just experimental. I wanted the flexibility in looking at volatility and this indicator gives you several ways to do so.
I haven't figured out the best way to use this yet but I suspect that as a form of entry confirmation indicator would be best.
If you find a way this works well for you please drop me a note. It would nice know someone found a way to use it successfully!
The options available are:
* Your source can be price or the ATR.
* It allows you to separate the volatility of the bearish and bullish candles and even allows you to produce differential.
* You can choose to run the result through any one of many smoothers.
With the above options you can look at:
* The normal volatility. That is not split into bearish and bullish components.
* The bearish and bullish volatility and the difference between them.
* The relative bearish and bullish volatility and the difference between them.
The "The relative bearish and bullish" is each one divided into the source before it was split into Up and Down or low/high divided by close which should make the max value roughly around 1.
The code is structured to easily drop into a bigger system so use it as a lone indicator or add the code to some bigger project you are creating. If you do integrate it into something else then send me a note as it would be nice to know it's being well used.
Enjoy and good luck!
MeanReversion by VolatilityMean reversion is a financial term for the assumption that an asset will return to its mean value.
This indicator calculate the volatility of an asset over a period of time and show the values of logRerturn, mean and standart deviations.
The default time period for volatility calculation is 252 bars at a "Daily" chart. At a "Daily" chart 252 bar means one trading-year.
See also:
MeanReversion by Logarithmic Returns
Standard Deviation Channel V.1Standard Deviation channel For TradingView V.1
Many thanks to and Made with help from @rumpypumpydumpy
█ - How to add the indicator-
You can “Boost” the tool if you like it, then scroll down on this page to "Add to favorite indicators" so it will be saved in your favorites. Easiest way to add to chart past that is simply copy the indicators name, Navigate to a chart, then paste the indicators name into your chart's "Indicators" tab. It should then be immediately added to the current chart. If your display is not large enough, when you first add your channel,, you may realize that you see labels appear, but no channel. Simply scroll backwards in time until the chart loads. TradingView needs to be able to see the data you would like the channel to read in order to plot and display correctly. This is a simple one or two mouse wheel scroll and it will appear.
You may notice a compression of price scale. IF this happens simply right click your right price axis, a menu will appear, select “Scale price chart only”, and "Auto (fits data to screen) This will release the scale compression and let you view the channel and price normally. Once your Channel is added, loaded, and ready to go, you can proceed to settings. In the top left corner of your main chart there will be a Indicator title, hover that and click on the gear icon to access the channels custom settings. You can also double click any of the active plots from the channel or averages on the chart, and gain access to the settings panel through that.
█ OVERVIEW
Settings explained -
Inputs and color choices
You can think of the settings panel as 3 separate sections.
First - Look and feel- You will have your Channels visual inputs, Simple Yes or No check boxes on whether you would like to display the visual items listed. You can choose to display the channel in a multitude of ways, with or without half deviations, with no 2nd, 3rd, or 4th deviations. This first section is your quick access control panel to the visual feel and display of the channel and its items.
Then below that you will see quick access color presets for each deviation and half deviations. You can choose to leave these as is, or you can choose custom colors per your preference.
The positive and negative Second deviations (+/-2std) are colored by positive and negative slope of channel. This will help to show overall trend, whether up or down, positive or negative. User can change the positive and negative slope colors if they would like.
Second, - Time and Regression - Next as you scroll down the settings panel you will encounter the Time and regression settings. In order for the channel to match the channel used widely in TOS, we had to Preset the look back lengths into the code because on Tradingview we have an “Continuous left edge of the chart”. We needed to tell the channel how far to look back and start calculating. The frame work for this time logic came initially from the channel that was developed years back by @corgalicious, We then took that time logic and re-worked it in order to fit the parameters that the widely used and popular TOS channel has.
Above the time frame length back inputs you will find a dropdown menu "Regression method type". This will offer different methods of regression and calculating the standard deviation from the center linear regression line. It is preset to “Population standard deviation” which will mimic the widely used TOS channel. There is also a choice for “Regression method standard error, or RMSE. This is a similar regression style, but will result in a tighter fitting, smaller deviation measurement and channel all around. As well as a multitude of other regression styles thanks to the genius of @rumpypumpydumpy
All the time presets were carefully chosen based off Pre set time frames TOS offers for their widely used Standard deviation channel, and time frames I had noted as widely used. You as the user can change those look back windows if you prefer through the input length settings. I recommend using the stock settings in most scenarios. Trading view has a 5000 bar look back limit, so we have implemented “Max lookbacks” inside the code to avoid any user error or confusion. The standard error of the sample mean is an estimate of how far the sample mean is likely to be from the population mean, whereas the standard deviation of the sample is the degree to which individuals within the sample differ from the sample mean. For longer time frames and sample sets I tend to use Population Standard Dev setting. For smaller sample sets I will go with Linreg RMSE setting. This is a personal preference. It is encouraged to try all of them and see what fits your trading style the best.
If the user would like to use a "Max bar lookback and plot the maximum allowed length on the current time frame, Simply select, "Use the full range of data allowed in max bars back for calculation?" This will automatically search back on the current time frame and plot the channel 4999 bars back. User will have to SCROLL BACK in order to fully load the channel into view. Again, Tradingview needs to see the candles you would like to plot on.
Third, - Finally at the bottom of the settings I have included Exponential moving average clouds. These are NOT enabled by default. If the user would like them enabled simply check "show momentum average clouds" and "Show Candle EMA". These are Multiple time frame moving average clouds consisting of 72/89 length 3, and 5min exponential moving averages. I use these to simply show the front or back side of a move and to find if trend is strong or weakening. These are not always needed so they are turned off by default.
█ CONCEPTS
Reversion and Repulsion-
You will find that the channel linear regression trend line has two characteristic's, Reversion to the mean, and Repulsion away from the mean. Price either seeks to aggressively return to the mean when it has exited a normal distribution, or price seeks to aggressively move away from the mean in times of momentum. Most seek to participate in the move through MAJOR WHOLE deviation levels in one scenario or the other.
The idea behind using a Standard deviation channel is to see extension and find where in the move we are. Are you extended out to 3 or 4 deviation's up or down? If so, you could start to think about reversion back to the mean. Have you had a violent move down to -3 or -4 deviations in a sell off? Maybe look at reversion back up toward the mean off a whole deviation break. Have you broken out of a normal distribution at +1 deviation and are building trend? maybe seek to join trend.
I have found most success by using a Split screen style layout. On the left chart most will have a 1min intraday channel showing, and on the left chart a 4hr channel showing. The idea is to mark your longer time frame deviations onto your intraday time frame, and use the intraday Channel to guide you through the higher time framed move. The move through +/- 1 deviation is a high momentum area in most names as price either seeks to return to the mean, or move strongly away from the mean.
█ Time periods
The channel has pre determined lookback presets for each major time frame. These have been preset in the code to mimic the widely used channel in TOS to the best of our ability.
Preset timeframe lookbacks include.
//intraday shorter time frames. 1/2min with 2day lookbacks
'1D-1Min' - Default= 2D, minval=1, maxval=5
'1D-2Min' - Default= 2D, minval=1, maxval=7
//intraday shorter time frames. 3/5min with 5day lookbacks. User can set shorter or longer if they choose, up to a 5000k bar look back depending on their Data tier level, Basic, Pro, Pro+, Premium etc.
'5D-3Min' - Default= 5D, minval=1, maxval=7
'5D-5Min' - Default= 5D, minval=1, maxval=20
// larger intraday time frames, 10/15min with 5day look backs.
'5D-10Min' - Default= 5D, minval=1, maxval=20
'5D-15Min' - Default= 5D, minval=1, maxval=60
// "Swing style time frames" 30/60 min with 10 and 20 day look back.
'10D-30Min' - Default= 10D, minval=1, maxval=60
'20D-1Hr' - Default= 20D, minval=1, maxval=90
//longer lookbacks for larger time frames using day lookback with the exception of week/month
'90D-2Hr' - Default = 90D, minval=1, maxval=180
'4h ' - Default = 180D,minval=1, maxval=4999
'6h' - Default = 36D, minval=1, maxval=252
'5Yr-W' - Default = 260W,minval=1, maxval=260
'1Yr-1D' - Default = 252D,minval=1, maxval=4999
'1Yr-1W' - Default = 52W, minval=1, maxval=480
'5Yr-1M' - Default = 60W, minval=1, maxval=480
█ Minimum Window Size
Note that on each time frame you MUST quickly scroll out to the first bar that the channel should start calculating on in order for the channel to populate on longer time frame series. This is under construction and as soon as there is a fix or other way around this, it will be addressed.
█ NOTES
Enjoy!
In the end I encourage any who tries the Channel to really sit down and spend some time playing around with the settings in order to find out how they like the Channel set up. I usually run the default settings on a intraday 5min chart, and then another instance of the study on a 4 hour chart. That way I can see granular intraday levels, and macro long term levels in the same view. See what fit's you the best, and how you like to trade. Most of all ENJOY!
Good luck -
JMF.
IMPORTANT INFO-
As always, the creator of this code is NOT a licensed investment advisor. No output of this tool is to be taken as investment advice or a recommendation to buy or sell any security.
Trading is risky, any one using this tool acknowledges they CAN LOSE some if not all of their initial investment even with this tool enabled.
User assumes ALL RESPONSIBILITY when using this tool in their technical analysis. There is NO GUARANTEE THAT THE USE OF THIS TOOL WILL RESULT IN PROFIT Use at your own risk.
MeanReversion by Logarithmic ReturnsMean reversion is a financial term for the assumption that an asset will return to its mean value.
This indicator calculate the logarithmic returns (logReturn) of an asset over a period of time and show the values of logRerturn, mean and standart deviations.
The default time period for logReturn calculation is 252 bars at a "Daily" chart. At a "Daily" chart 252 bar means one trading-year.
See also:
MeanReversion by Volatility
VWAP Previous VWAP WMQY StdDev Extensions Nadro StyleDisplays Multi-TF VWAP with Std Dev Bands.
Developing VWAP and Std Dev Bands
Previous VWAP and Std Dev Bands
Previous VWAP Extensions
Some Examples
VolatilityCone by ImpliedVolatilityThis volatility cone draws the implied volatility as standard deviations from a measurement date.
For best results set measurement date to high volume bars.
How to use:
1) Select VolatilityCone from Indicators
2) Click to the chart to set the measurement date
3) Determine the impliedvolatility for the measurement date of your symbol
e.g.
For S&P500 use VIX value at measurement date for implied volatility
ZenBot Signals - Trend StrengthI developed this indicator as a "regime detection" for my algo trading bot. It uses the ADX +/- values with a few twists.
- If ADX DI+ is over 30 and DI- is below 20 and falling (inverse for shorts)
- Price action rising/falling thru various VWAP standard deviations indicates a strong trend break
- Some other custom juju (open source so have fun).
I use this primarily to monitor the SPY index as a backdrop for my long and short trades. If the colored line below price bars is red or green, a strong trend is present and there is a decent trade environment.
VWAP Market Session AnchoredVWAP Market Session Anchored differs from the traditional VWAP or VWAP Auto Anchored indicator in that the Volume Weighted Average Price calculation is automatically anchored to four major market session starts: Sydney, London, Tokyo, New York.
Settings
Source: the source for the VWAP calculation.
Offset: changing this number will move the VWAP either Forwards or Backwards, relative to the current market. Zero is the default.
Band: enabling this will show Standard Deviation bands.
Band Multiplier: the value the Standard Deviation bands will be multiplied by before being plotted on the chart.
Sessions : enabling the sessions will plot the respective anchored VWAP on chart.
Custom: enabling this will show a custom user-defined session.
Custom UTC : the custom session is defined by a starting UTC hour followed by the ending UTC hour.
Usage
Similar to the traditional VWAP, VWAP Market Session Anchored is a technical analysis tool used to measure the average price weighted by volume. VWAP Market Session Anchored can be used to identify the trend during a specific market session.
Limitations
When setting a custom session, be mindful that calculations are based off of the Coordinated Universal Time (UTC) time, you must convert your local time zone to UTC in order to have an accurate representation of your custom session.
It is not recommended to use this indicator on timeframes above 1 hour as market sessions only last a few hours.
Gaussian Filter ModifiedAn effort to enhance auto-trading based on Gaussian Filter with Standard Deviation Filtering, Trading True Range and Smoothed SMA was added to remove noise contributing to ranging markets and unwanted entries against established trend.
Gaussian parameters need to be adjusted for different asset pair to find its own "signature", then filter out bad entry with TTR and SMA.
*Credits to Loxx for his work on Gaussian Filter
Asymmetric Dispersion High Lowdear fellows,
this indicator is an effort to determine the range where the prices are likely to fall within in the current candle.
how it is calculated
1. obtain
a. gain from the open to the high
b. loss from the open to the low
in the last 20 (by default) candles and
in the last 200 (10*20 by default) candles
2. perform
a. the geometric average (sma of the log returns) over these gains and losses
b. their respective standard deviation
3. plot from the open of each candle
a. the average + 2 standard deviations (2 by default) of the short window size
b. same for the long window size (which is overlapped)
what it shows
1. where the current candle is likely to move with 95% likelyhood
how it can be interpreted
1. a gauge for volatility in the short and long term
2. a visual inbalance between likelyhood to go up or down according to dispersion in relation to current prices or candle open.
3. a confirmation of crossings of, for instance, support and resistances once the cloud is completely above or below.
in regard to bollinger bands (which are and excellent well proven indicator)
1. it segregates upward moves from the downward ones.
2. it is hardly crossed by prices
3. it is centered on the current candle open, instead of the moving average.
we welcome feedback and critic.
best regards and success wishes.
Quantitative mean reversion v4The code uses the concept of mean reversion. Mean reversion suggests that price over a period of time reverts back to its statistical mean. In simple terms, it means if a price has drifted apart from the statistical mean, after a certain amount of time, it will revert back to its statistical mean. This drift is measured via z-score. When the z-score value is high, the price is expected to revert. Besides, the higher the time frame you use, the lesser the drift is, so reduce the z-score in the tabs if you use higher time frames, else, vice-versa.
Based on the parameters, the code will provide a trade signal - both long and short, and entry and exit. You can use notifications for alerts. Please use the parameters in the options to find the best combinations for your stocks.
In the properties, you can use your own brokers commission, capital, to see if the strategy is profitable for your ticker in the long run or not. This code has been tested for profits for various assets in both crypto - Bitcoin futures , Ethereum futures -, and stocks - AMD , Apple , MSFT , etc.
This is not get rich quick scheme, and you have to be patient with it for the long run.
If you have any query, please feel free to ask in the comments sections.
If you want some new changes, please feel free to suggest
Currently, I am optimising the maximum time for holding a trade. Till that's completed, use this and please feel free to leave a feedback to make it better
GB Gilt Yield CurveWith thanks to @longfiat whose US Treasury Yield Curve served as the basis for this indicator
This is created very quickly to provide a sense of the GB Gilt Yield curve in light of government induced market dysfunction as a result of an ill-conceived mini-budget.
Note that I omitted GB04Y, GB06Y, GB08Y, GB09Y and GB12Y to avoid overcrowding the chart with excess information and thereby render the indicator more readily usable.
Probability Cloud BASIC [@AndorraInvestor]🔮☁️
This is the BASIC version of the PROBABILITY CLOUD indicator.
It is an evolution beyond traditional standard deviation probabilistic indicators only using bands or channels.
The new PROBABILITY CLOUD graphic representation with customizable transparent layers is based on -2 / +2 standard deviation calculated using 20 fixed predetermined time periods, and is available in several calculation MODES:
SMA , EMA , WMA , VWMA , VWMA & VAWMA
The indicator is designed to let the trader visually understand the probabilistic depth of past, present and future price action, and its evolution over time.
Looking forward to your comments and feedback to guide me on future updates!
🙏 Big THANKS @Electrified for letting me use his work on Deviation Bands/ as a starting point for my first script.
Strength of Divergence Across Multiple IndicatorsOverview:
One-stop shop for all your divergence needs, including:
(1) A single metric for divergence strength across multiple indicators.
(2) Labels that make it easy to spot where the truly strong divergence is by showing the overall divergence strength value along with the number of divergent indicators. Hovering over the label shows a breakdown of each divergent indicator and its individual divergence strength value.
(3) Fully customizable, including inputs for pivot lengths, divergence types, and weights for every component of the divergence strength calculation. This allows you to quickly and easily optimize the output for any chart. Don't worry, the default settings will have you covered if you're not interested in what's going on under the hood.
The Divergence Strength Calculation:
The total divergence strength value is the sum of the divergence strengths of all indicators for which divergence was detected at a given bar. Each indicator's individual divergence strength is comprised of two basic components: (1) |ΔPrice| - the magnitude of the change in price over the divergence period (pivot-to-pivot), and (2) |ΔIndicator| - the magnitude of the change in indicator value over the divergence period.
Because different indicators' scales and volatility can vary greatly, the Δ values are expressed in terms of standard deviation to ensure that the values are meaningful and equitable across all indicators and assets/instruments/currency pairs, etc:
|ΔIndicator| = |indicator_value_1 - indicator_value_2| / 2 * StDev(indicator_series,100)
Calculation Weights:
All components of the calculation are weighted and can be modified on the Inputs page in settings (weights are simply multipliers). For example, if you think hidden divergence should carry less weight than regular divergence, you can assign it a lesser weight. Or if you think RSI divergence is worth more than OBV divergence, you can adjust their weights accordingly. List of weights:
Regular divergence weight - default = 1
Hidden divergence weight - default = 1
ΔPrice weight - default = 0.5 (multiplied by the ΔPrice component)
ΔIndicator weight - default = 1.5 (multiplied by the ΔIndicator component)
RSI weight - default = 1.1
OBV weight - default = 0.8
MACD weight - default = 0.9
STOCH weight - default = 0.9
Development for additional indicators is ongoing, as is research into the optimal weight configuration(s).
Other Inputs:
Pivot lengths - specify the number of bars before and after each pivot high/low to consider it a valid candidate for divergence.
Lookback bars and Lookback pivots - specify the number of bars or the number of pivots to look back across.
Price sources - specify separate price sources for bullish and bearish divergence
Display settings - specify how lines and labels should display, including which divergence strength values should show the largest labels. Include/exclude specific divergence types and indicators.
Please report any bugs, or let me know if you have any enhancement suggestions or requests for additional indicators.
@reees
Variance (Welford) [Loxx]The standard deviation is a measure of how much a dataset differs from its mean; it tells us how dispersed the data are. A dataset that’s pretty much clumped around a single point would have a small standard deviation, while a dataset that’s all over the map would have a large standard deviation. You can. use this calculation for other indicators.
Given a sample the standard deviation is defined as the square root of the variance
Here you can find a Welford’s method for computing (single pass method) that avoids errors in some cases (if the variance is small compared to the square of the mean, and computing the difference leads catastrophic cancellation where significant leading digits are eliminated and the result has a large relative error)
Read more here: jonisalonen.com
Incliuded
Loxx's Expanded Source Types
STD-Adaptive T3 [Loxx]STD-Adaptive T3 is a standard deviation adaptive T3 moving average filter. This indicator acts more like a trend overlay indicator with gradient coloring.
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
Loxx's Expanded Source Types
STD-Filtered, Variety FIR Digital Filters w/ ATR Bands [Loxx]STD-Filtered, Variety FIR Digital Filters w/ ATR Bands is a FIR Digital Filter indicator with ATR bands. This indicator contains 12 different digital filters. Some of these have already been covered by indicators that I've recently posted. The difference here is that this indicator has ATR bands, allows for frequency filtering, adds a frequency multiplier, and attempts show causality by lagging price input by 1/2 the period input during final application of weights. Period is restricted to even numbers.
The 3 most important parameters are the frequency cutoff, the filter window type and the "causal" parameter.
Included filter types:
- Hamming
- Hanning
- Blackman
- Blackman Harris
- Blackman Nutall
- Nutall
- Bartlet Zero End Points
- Bartlet Hann
- Hann
- Sine
- Lanczos
- Flat Top
Frequency cutoff can vary between 0 and 0.5. General rule is that the greater the cutoff is the "faster" the filter is, and the smaller the cutoff is the smoother the filter is.
You can read more about discrete-time signal processing and some of the windowing functions in this indicator here:
Window function
Window Functions and Their Applications in Signal Processing
What are FIR Filters?
In discrete-time signal processing, windowing is a preliminary signal shaping technique, usually applied to improve the appearance and usefulness of a subsequent Discrete Fourier Transform. Several window functions can be defined, based on a constant (rectangular window), B-splines, other polynomials, sinusoids, cosine-sums, adjustable, hybrid, and other types. The windowing operation consists of multipying the given sampled signal by the window function. For trading purposes, these FIR filters act as advanced weighted moving averages.
A finite impulse response (FIR) filter is a filter whose impulse response (or response to any finite length input) is of finite duration, because it settles to zero in finite time. This is in contrast to infinite impulse response (IIR) filters, which may have internal feedback and may continue to respond indefinitely (usually decaying).
The impulse response (that is, the output in response to a Kronecker delta input) of an Nth-order discrete-time FIR filter lasts exactly {\displaystyle N+1}N+1 samples (from first nonzero element through last nonzero element) before it then settles to zero.
FIR filters can be discrete-time or continuous-time, and digital or analog.
A FIR filter is (similar to, or) just a weighted moving average filter, where (unlike a typical equally weighted moving average filter) the weights of each delay tap are not constrained to be identical or even of the same sign. By changing various values in the array of weights (the impulse response, or time shifted and sampled version of the same), the frequency response of a FIR filter can be completely changed.
An FIR filter simply CONVOLVES the input time series (price data) with its IMPULSE RESPONSE. The impulse response is just a set of weights (or "coefficients") that multiply each data point. Then you just add up all the products and divide by the sum of the weights and that is it; e.g., for a 10-bar SMA you just add up 10 bars of price data (each multiplied by 1) and divide by 10. For a weighted-MA you add up the product of the price data with triangular-number weights and divide by the total weight.
What is a Standard Deviation Filter?
If price or output or both don't move more than the (standard deviation) * multiplier then the trend stays the previous bar trend. This will appear on the chart as "stepping" of the moving average line. This works similar to Super Trend or Parabolic SAR but is a more naive technique of filtering.
Included
Bar coloring
Loxx's Expanded Source Types
Signals
Alerts
Related indicators
STD/C-Filtered, N-Order Power-of-Cosine FIR Filter
STD/C-Filtered, Power-of-Cosine FIR Filter
STD/C-Filtered, Truncated Taylor Family FIR Filter
STD/Clutter-Filtered, Variety FIR Filters
STD/Clutter-Filtered, Kaiser Window FIR Digital Filter
STD/C-Filtered, N-Order Power-of-Cosine FIR Filter [Loxx]STD/C-Filtered, N-Order Power-of-Cosine FIR Filter is a Discrete-Time, FIR Digital Filter that uses Power-of-Cosine Family of FIR filters. This is an N-order algorithm that turns the following indicator from a static max 16 orders to a N orders, but limited to 50 in code. You can change the top end value if you with to higher orders than 50, but the signal is likely too noisy at that level. This indicator also includes a clutter and standard deviation filter.
See the static order version of this indicator here:
STD/C-Filtered, Power-of-Cosine FIR Filter
Amplitudes for STD/C-Filtered, N-Order Power-of-Cosine FIR Filter:
What are FIR Filters?
In discrete-time signal processing, windowing is a preliminary signal shaping technique, usually applied to improve the appearance and usefulness of a subsequent Discrete Fourier Transform. Several window functions can be defined, based on a constant (rectangular window), B-splines, other polynomials, sinusoids, cosine-sums, adjustable, hybrid, and other types. The windowing operation consists of multipying the given sampled signal by the window function. For trading purposes, these FIR filters act as advanced weighted moving averages.
What is Power-of-Sine Digital FIR Filter?
Also called Cos^alpha Window Family. In this family of windows, changing the value of the parameter alpha generates different windows.
f(n) = math.cos(alpha) * (math.pi * n / N) , 0 ≤ |n| ≤ N/2
where alpha takes on integer values and N is a even number
General expanded form:
alpha0 - alpha1 * math.cos(2 * math.pi * n / N)
+ alpha2 * math.cos(4 * math.pi * n / N)
- alpha3 * math.cos(4 * math.pi * n / N)
+ alpha4 * math.cos(6 * math.pi * n / N)
- ...
Special Cases for alpha:
alpha = 0: Rectangular window, this is also just the SMA (not included here)
alpha = 1: MLT sine window (not included here)
alpha = 2: Hann window (raised cosine = cos^2)
alpha = 4: Alternative Blackman (maximized roll-off rate)
This indicator contains a binomial expansion algorithm to handle N orders of a cosine power series. You can read about how this is done here: The Binomial Theorem
What is Pascal's Triangle and how was it used here?
In mathematics, Pascal's triangle is a triangular array of the binomial coefficients that arises in probability theory, combinatorics, and algebra. In much of the Western world, it is named after the French mathematician Blaise Pascal, although other mathematicians studied it centuries before him in India, Persia, China, Germany, and Italy.
The rows of Pascal's triangle are conventionally enumerated starting with row n = 0 at the top (the 0th row). The entries in each row are numbered from the left beginning with k=0 and are usually staggered relative to the numbers in the adjacent rows. The triangle may be constructed in the following manner: In row 0 (the topmost row), there is a unique nonzero entry 1. Each entry of each subsequent row is constructed by adding the number above and to the left with the number above and to the right, treating blank entries as 0. For example, the initial number in the first (or any other) row is 1 (the sum of 0 and 1), whereas the numbers 1 and 3 in the third row are added to produce the number 4 in the fourth row.
Rows of Pascal's Triangle
0 Order: 1
1 Order: 1 1
2 Order: 1 2 1
3 Order: 1 3 3 1
4 Order: 1 4 6 4 1
5 Order: 1 5 10 10 5 1
6 Order: 1 6 15 20 15 6 1
7 Order: 1 7 21 35 35 21 7 1
8 Order: 1 8 28 56 70 56 28 8 1
9 Order: 1 9 36 34 84 126 126 84 36 9 1
10 Order: 1 10 45 120 210 252 210 120 45 10 1
11 Order: 1 11 55 165 330 462 462 330 165 55 11 1
12 Order: 1 12 66 220 495 792 924 792 495 220 66 12 1
13 Order: 1 13 78 286 715 1287 1716 1716 1287 715 286 78 13 1
For a 12th order Power-of-Cosine FIR Filter
1. We take the coefficients from the Left side of the 12th row
1 13 78 286 715 1287 1716 1716 1287 715 286 78 13 1
2. We slice those in half to
1 13 78 286 715 1287 1716
3. We reverse the array
1716 1287 715 286 78 13 1
This is our array of alphas: alpha1, alpha2, ... alphaN
4. We then pull alpha one from the previous order, order 11, the middle value
11 Order: 1 11 55 165 330 462 462 330 165 55 11 1
The middle value is 462, this value becomes our alpha0 in the calculation
5. We apply these alphas to the cosine calculations
example: + alpha4 * math.cos(6 * math.pi * n / N)
6. We then divide by the sum of the alphas to derive our final coefficient weighting kernel
**This is only useful for orders that are EVEN, if you use odd ordering, the following are the coefficient outputs and these aren't useful since they cancel each other out and result in a value of zero. See below for an odd numbered oder and compare with the amplitude of the graphic posted above of the even order amplitude:
What is a Standard Deviation Filter?
If price or output or both don't move more than the (standard deviation) * multiplier then the trend stays the previous bar trend. This will appear on the chart as "stepping" of the moving average line. This works similar to Super Trend or Parabolic SAR but is a more naive technique of filtering.
What is a Clutter Filter?
For our purposes here, this is a filter that compares the slope of the trading filter output to a threshold to determine whether to shift trends. If the slope is up but the slope doesn't exceed the threshold, then the color is gray and this indicates a chop zone. If the slope is down but the slope doesn't exceed the threshold, then the color is gray and this indicates a chop zone. Alternatively if either up or down slope exceeds the threshold then the trend turns green for up and red for down. Fro demonstration purposes, an EMA is used as the moving average. This acts to reduce the noise in the signal.
Included
Bar coloring
Loxx's Expanded Source Types
Signals
Alerts
STD/C-Filtered, Power-of-Cosine FIR Filter [Loxx]STD/C-Filtered, Power-of-Cosine FIR Filter is a Discrete-Time, FIR Digital Filter that uses Power-of-Cosine Family of FIR filters. This indicator also includes a clutter and standard deviation filter.
Amplitudes
What are FIR Filters?
In discrete-time signal processing, windowing is a preliminary signal shaping technique, usually applied to improve the appearance and usefulness of a subsequent Discrete Fourier Transform. Several window functions can be defined, based on a constant (rectangular window), B-splines, other polynomials, sinusoids, cosine-sums, adjustable, hybrid, and other types. The windowing operation consists of multipying the given sampled signal by the window function. For trading purposes, these FIR filters act as advanced weighted moving averages.
What is Power-of-Sine Digital FIR Filter?
Also called Cos^alpha Window Family. In this family of windows, changing the value of the parameter alpha generates different windows.
f(n) = math.cos(alpha) * (math.pi * n / N) , 0 ≤ |n| ≤ N/2
where alpha takes on integer values and N is a even number
General expanded form:
alpha0 - alpha1 * math.cos(2 * math.pi * n / N)
+ alpha2 * math.cos(4 * math.pi * n / N)
- alpha3 * math.cos(4 * math.pi * n / N)
+ alpha4 * math.cos(6 * math.pi * n / N)
- ...
Special Cases for alpha:
alpha = 0: Rectangular window, this is also just the SMA (not included here)
alpha = 1: MLT sine window (not included here)
alpha = 2: Hann window (raised cosine = cos^2)
alpha = 4: Alternative Blackman (maximized roll-off rate)
For this indicator, I've included alpha values from 2 to 16
What is a Standard Devaition Filter?
If price or output or both don't move more than the (standard deviation) * multiplier then the trend stays the previous bar trend. This will appear on the chart as "stepping" of the moving average line. This works similar to Super Trend or Parabolic SAR but is a more naive technique of filtering.
What is a Clutter Filter?
For our purposes here, this is a filter that compares the slope of the trading filter output to a threshold to determine whether to shift trends. If the slope is up but the slope doesn't exceed the threshold, then the color is gray and this indicates a chop zone. If the slope is down but the slope doesn't exceed the threshold, then the color is gray and this indicates a chop zone. Alternatively if either up or down slope exceeds the threshold then the trend turns green for up and red for down. Fro demonstration purposes, an EMA is used as the moving average. This acts to reduce the noise in the signal.
Included
Bar coloring
Loxx's Expanded Source Types
Signals
Alerts
STD/C-Filtered, Truncated Taylor Family FIR Filter [Loxx]STD/C-Filtered, Truncated Taylor Family FIR Filter is a FIR Digital Filter that uses Truncated Taylor Family of Windows. Taylor functions are obtained by adding a weighted-cosine series to a constant (called a pedestal). A simpler form of these functions can be obtained by dropping some of the higher-order terms in the Taylor series expansion. If all other terms, except for the first two significant ones, are dropped, a truncated Taylor function is obtained. This is a generalized window that is expressed as:
(1 + K) / 2 + (1 - K) / 2 * math.cos(2.0 * math.pi *n / N) where 0 ≤ |n| ≤ N/2
Here k can take the values in the range 0≤k≤1. We note that the Hann 0 ≤ |n| ≤ window is a special case of the truncated Taylor family with k = 0 and Rectangular 0 ≤ |n| ≤ window (SMA) is a special case of the truncated Taylor family with k = 1.
Truncated Taylor Family of Windows amplitudes for this indicator with K = 0.5
This indicator also includes Standard Deviation and Clutter filtering.
What is a Standard Devaition Filter?
If price or output or both don't move more than the (standard deviation) * multiplier then the trend stays the previous bar trend. This will appear on the chart as "stepping" of the moving average line. This works similar to Super Trend or Parabolic SAR but is a more naive technique of filtering.
What is a Clutter Filter?
For our purposes here, this is a filter that compares the slope of the trading filter output to a threshold to determine whether to shift trends. If the slope is up but the slope doesn't exceed the threshold, then the color is gray and this indicates a chop zone. If the slope is down but the slope doesn't exceed the threshold, then the color is gray and this indicates a chop zone. Alternatively if either up or down slope exceeds the threshold then the trend turns green for up and red for down. Fro demonstration purposes, an EMA is used as the moving average. This acts to reduce the noise in the signal.
Included
Bar coloring
Loxx's Expanded Source Types
Signals
Alerts
STD- and Clutter-Filtered, Non-Lag Moving Average [Loxx]STD- and Clutter-Filtered, Non-Lag Moving Average is a Weighted Moving Average with a minimal lag using a damping cosine wave as the line of weight coefficients. The indicator has two filters. They are static (in points) and dynamic (expressed as a decimal). They allow cutting the price noise giving a stepped shape to the Moving Average. Moreover, there is the possibility to highlight the trend direction by color. This also includes a standard deviation and clutter filter. This filter is a FIR filter.
What is a Generic or Direct Form FIR Filter?
In signal processing, a finite impulse response (FIR) filter is a filter whose impulse response (or response to any finite length input) is of finite duration, because it settles to zero in finite time. This is in contrast to infinite impulse response (IIR) filters, which may have internal feedback and may continue to respond indefinitely (usually decaying).
The impulse response (that is, the output in response to a Kronecker delta input) of an Nth-order discrete-time FIR filter lasts exactly {\displaystyle N+1}N+1 samples (from first nonzero element through last nonzero element) before it then settles to zero.
FIR filters can be discrete-time or continuous-time, and digital or analog.
A FIR filter is (similar to, or) just a weighted moving average filter, where (unlike a typical equally weighted moving average filter) the weights of each delay tap are not constrained to be identical or even of the same sign. By changing various values in the array of weights (the impulse response, or time shifted and sampled version of the same), the frequency response of a FIR filter can be completely changed.
An FIR filter simply CONVOLVES the input time series (price data) with its IMPULSE RESPONSE. The impulse response is just a set of weights (or "coefficients") that multiply each data point. Then you just add up all the products and divide by the sum of the weights and that is it; e.g., for a 10-bar SMA you just add up 10 bars of price data (each multiplied by 1) and divide by 10. For a weighted-MA you add up the product of the price data with triangular-number weights and divide by the total weight.
What is a Clutter Filter?
For our purposes here, this is a filter that compares the slope of the trading filter output to a threshold to determine whether to shift trends. If the slope is up but the slope doesn't exceed the threshold, then the color is gray and this indicates a chop zone. If the slope is down but the slope doesn't exceed the threshold, then the color is gray and this indicates a chop zone. Alternatively if either up or down slope exceeds the threshold then the trend turns green for up and red for down. Fro demonstration purposes, an EMA is used as the moving average. This acts to reduce the noise in the signal.
What is a Dual Element Lag Reducer?
Modifies an array of coefficients to reduce lag by the Lag Reduction Factor uses a generic version of a Kalman velocity component to accomplish this lag reduction is achieved by applying the following to the array:
2 * coeff - coeff
The response time vs noise battle still holds true, high lag reduction means more noise is present in your data! Please note that the beginning coefficients which the modifying matrix cannot be applied to (coef whose indecies are < LagReductionFactor) are simply multiplied by two for additional smoothing .
Included
Bar coloring
Loxx's Expanded Source Types
Signals
Alerts
STD-Filtered, Ultra Low Lag Moving Average [Loxx]STD-Filtered, Ultra Low Lag Moving Average is a FIR filter that smooths price using a low-pass filtering with weights derived from a normalized cardinal since function. This indicator attempts to reduce lag to an extreme degree. Try this on various time frames with various Type inputs, 0 is the default, so see where the sweet spot is for your trading style.
What is a Finite Impulse Response Filter?
In signal processing, a finite impulse response (FIR) filter is a filter whose impulse response (or response to any finite length input) is of finite duration, because it settles to zero in finite time. This is in contrast to infinite impulse response (IIR) filters, which may have internal feedback and may continue to respond indefinitely (usually decaying).
The impulse response (that is, the output in response to a Kronecker delta input) of an Nth-order discrete-time FIR filter lasts exactly {\displaystyle N+1}N+1 samples (from first nonzero element through last nonzero element) before it then settles to zero.
FIR filters can be discrete-time or continuous-time, and digital or analog.
A FIR filter is (similar to, or) just a weighted moving average filter, where (unlike a typical equally weighted moving average filter) the weights of each delay tap are not constrained to be identical or even of the same sign. By changing various values in the array of weights (the impulse response, or time shifted and sampled version of the same), the frequency response of a FIR filter can be completely changed.
An FIR filter simply CONVOLVES the input time series (price data) with its IMPULSE RESPONSE. The impulse response is just a set of weights (or "coefficients") that multiply each data point. Then you just add up all the products and divide by the sum of the weights and that is it; e.g., for a 10-bar SMA you just add up 10 bars of price data (each multiplied by 1) and divide by 10. For a weighted-MA you add up the product of the price data with triangular-number weights and divide by the total weight.
Ultra Low Lag Moving Average's weights are designed to have MAXIMUM possible smoothing and MINIMUM possible lag compatible with as-flat-as-possible phase response.
What is Normalized Cardinal Sine?
The sinc function sinc(x), also called the "sampling function," is a function that arises frequently in signal processing and the theory of Fourier transforms.
In mathematics, the historical unnormalized sinc function is defined for x ≠ 0 by
sinc x = sinx / x
In digital signal processing and information theory, the normalized sinc function is commonly defined for x ≠ 0 by
sinc x = sin(pi * x) / (pi * x)
How this works, (easy mode)
1. Use a HA or HAB source type
2. The lower the Type value the smoother the moving average
3. Standard deviation stepping is added to further reduce noise
Included
Bar coloring
Signals
Alerts
Loxx's Expanded Source Types