DynamicFunctionsLibrary "DynamicFunctions"
Custom Dynamic functions that allow an adaptive calculation beginning from the first bar
RoC(src, period)
Dynamic RoC
Parameters:
src (float) : and period
Custom function to calculate the actual period considering non-na source values
period (int)
dynamicMedian(src, length)
Dynamic Median
Parameters:
src (float) : and length
length (int)
kernelRegression(src, bandwidth, kernel_type)
Dynamic Kernel Regression Calculation Uses either of the following inputs for kernel_type: Epanechnikov Logistic Wave
Parameters:
src (float)
bandwidth (int)
kernel_type (string)
waveCalculation(source, bandwidth, width)
Use together with kernelRegression function to get chart applicable band
Parameters:
source (float)
bandwidth (int)
width (float)
Rsi(src, length)
Dynamic RSI function
Parameters:
src (float)
length (int)
dynamicStdev(src, period)
Dynamic SD function
Parameters:
src (float)
period (int)
stdv_bands(src, length, mult)
Dynamic SD Bands
Parameters:
src (float)
length (int)
mult (float)
Returns: Basis, Positive SD, Negative SD
Adx(dilen, adxlen)
Dynamic ADX
Parameters:
dilen (int)
adxlen (int)
Returns: adx
Atr(length)
Dynamic ATR
Parameters:
length (int)
Returns: ATR
Macd(source, fastLength, slowLength, signalSmoothing)
Dynamic MACD
Parameters:
source (float)
fastLength (int)
slowLength (int)
signalSmoothing (int)
Returns: macdLine, signalLine, histogram

# Adaptivelookback

DynamicMAsLibrary "DynamicMAs"
Custom MA's that allow a dynamic calculation beginning from the first bar, irrespective of lookback period.
SMA(src, length)
Dynamic SMA
Parameters:
src (float)
length (int)
EMA(src, length)
Dynamic EMA
Parameters:
src (float)
length (int)
DEMA(src, length)
Dynamic DEMA
Parameters:
src (float)
length (int)
TEMA(src, length)
Dynamic TEMA
Parameters:
src (float)
length (int)
WMA(src, length)
Dynamic WMA
Parameters:
src (float)
length (int)
HMA(src, length)
Dynamic HMA
Parameters:
src (float)
length (int)
VWMA(src, length)
Dynamic VWMA
Parameters:
src (float)
length (int)
SMMA(src, length)
Dynamic SMMA
Parameters:
src (float)
length (int)
LSMA(src, length)
Dynamic LSMA
Parameters:
src (float)
length (int)
ALMA(src, length, offset_sigma, sigma)
Dynamic ALMA
Parameters:
src (float)
length (int)
offset_sigma (float)
sigma (float)
HyperMA(src, length)
Dynamic HyperbolicMA
Parameters:
src (float)
length (int)

Optimal Length BackTester [YinYangAlgorithms]This Indicator allows for a ‘Optimal Length’ to be inputted within the Settings as a Source. Unlike most Indicators and/or Strategies that rely on either Static Lengths or Internal calculations for the length, this Indicator relies on the Length being derived from an external Indicator in the form of a Source Input.
This may not sound like much, but this application may allows limitless implementations of such an idea. By allowing the input of a Length within a Source Setting you may have an ‘Optimal Length’ that adjusts automatically without the need for manual intervention. This may allow for Traditional and Non-Traditional Indicators and/or Strategies to allow modifications within their settings as well to accommodate the idea of this ‘Optimal Length’ model to create an Indicator and/or Strategy that adjusts its length based on the top performing Length within the current Market Conditions.
This specific Indicator aims to allow backtesting with an ‘Optimal Length’ inputted as a ‘Source’ within the Settings.
This ‘Optimal Length’ may be used to display and potentially optimize multiple different Traditional Indicators within this BackTester. The following Traditional Indicators are included and available to be backtested with an ‘Optimal Length’ inputted as a Source in the Settings:
Moving Average; expressed as either a: Simple Moving Average, Exponential Moving Average or Volume Weighted Moving Average
Bollinger Bands; expressed based on the Moving Average Type
Donchian Channels; expressed based on the Moving Average Type
Envelopes; expressed based on the Moving Average Type
Envelopes Adjusted; expressed based on the Moving Average Type
All of these Traditional Indicators likewise may be displayed with multiple ‘Optimal Lengths’. They have the ability for multiple different ‘Optimal Lengths’ to be inputted and displayed, such as:
Fast Optimal Length
Slow Optimal Length
Neutral Optimal Length
By allowing for the input of multiple different ‘Optimal Lengths’ we may express the ‘Optimal Movement’ of such an expressed Indicator based on different Time Frames and potentially also movement based on Fast, Slow and Neutral (Inclusive) Lengths.
This in general is a simple Indicator that simply allows for the input of multiple different varieties of ‘Optimal Lengths’ to be displayed in different ways using Tradition Indicators. However, the idea and model of accepting a Length as a Source is unique and may be adopted in many different forms and endless ideas.
Tutorial:
You may add an ‘Optimal Length’ within the Settings as a ‘Source’ as followed in the example above. This Indicator allows for the input of a:
Neutral ‘Optimal Length’
Fast ‘Optimal Length’
Slow ‘Optimal Length’
It is important to account for all three as they generally encompass different min/max length values and therefore result in varying ‘Optimal Length’s’.
For instance, say you’re calculating the ‘Optimal Length’ and you use:
Min: 1
Max: 400
This would therefore be scanning for 400 (inclusive) lengths.
As a general way of calculating you may assume the following for which lengths are being used within an ‘Optimal Length’ calculation:
Fast: 1 - 199
Slow: 200 - 400
Neutral: 1 - 400
This allows for the calculation of a Fast and Slow length within the predetermined lengths allotted. However, it likewise allows for a Neutral length which is inclusive to all lengths alloted and may be deemed the ‘Most Accurate’ for these reasons. However, just because the Neutral is inclusive to all lengths, doesn’t mean the Fast and Slow lengths are irrelevant. The Fast and Slow length inputs may be useful for seeing how specifically zoned lengths may fair, and likewise when they cross over and/or under the Neutral ‘Optimal Length’.
This Indicator features the ability to display multiple different types of Traditional Indicators within the ‘Display Type’.
We will go over all of the different ‘Display Types’ with examples on how using a Fast, Slow and Neutral length would impact it:
Simple Moving Average:
In this example above have the Fast, Slow and Neutral Optimal Length formatted as a Slow Moving Average. The first example is on the 15 minute Time Frame and the second is on the 1 Day Time Frame, demonstrating how the length changes based on the Time Frame and the effects it may have.
Here we can see that by inputting ‘Optimal Lengths’ as a Simple Moving Average we may see moving averages that change over time with their ‘Optimal Lengths’. These lengths may help identify Support and/or Resistance locations. By using an 'Optimal Length' rather than a static length, we may create a Moving Average which may be more accurate as it attempts to be adaptive to current Market Conditions.
Bollinger Bands:
Bollinger Bands are a way to see a Simple Moving Average (SMA) that then uses Standard Deviation to identify how much deviation has occurred. This Deviation is then Added and Subtracted from the SMA to create the Bollinger Bands which help Identify possible movement zones that are ‘within range’. This may mean that the price may face Support / Resistance when it reaches the Outer / Inner bounds of the Bollinger Bands. Likewise, it may mean the Price is ‘Overbought’ when outside and above or ‘Underbought’ when outside and below the Bollinger Bands.
By applying All 3 different types of Optimal Lengths towards a Traditional Bollinger Band calculation we may hope to see different ranges of Bollinger Bands and how different lookback lengths may imply possible movement ranges on both a Short Term, Long Term and Neutral perspective. By seeing these possible ranges you may have the ability to identify more levels of Support and Resistance over different lengths and Trading Styles.
Donchian Channels:
Above you’ll see two examples of Machine Learning: Optimal Length applied to Donchian Channels. These are displayed with both the 15 Minute Time Frame and the 1 Day Time Frame.
Donchian Channels are a way of seeing potential Support and Resistance within a given lookback length. They are a way of withholding the High’s and Low’s of a specific lookback length and looking for deviation within this length. By applying a Fast, Slow and Neutral Machine Learning: Optimal Length to these Donchian Channels way may hope to achieve a viable range of High’s and Low’s that one may use to Identify Support and Resistance locations for different ranges of Optimal Lengths and likewise potentially different Trading Strategies.
Envelopes / Envelopes Adjusted:
Envelopes are an interesting one in the sense that they both may be perceived as useful; however we deem that with the use of an ‘Optimal Length’ that the ‘Envelopes Adjusted’ may work best. We will start with examples of the Traditional Envelope then showcase the Adjusted version.
Envelopes:
As you may see, a Traditional form of Envelopes even produced with a Machine Learning: Optimal Length may not produce optimal results. Unfortunately this may occur with some Traditional Indicators and they may need some adjustments as you’ll notice with the ‘Envelopes Adjusted’ version. However, even without the adjustments, these Envelopes may be useful for seeing ‘Overbought’ and ‘Oversold’ locations within a Machine Learning: Optimal Length standpoint.
Envelopes Adjusted:
By adding an adjustment to these Envelopes, we may hope to better reflect our Optimal Length within it. This is caused by adding a ratio reflection towards the current length of the Optimal Length and the max Length used. This allows for the Fast and Neutral (and potentially Slow if Neutral is greater) to achieve a potentially more accurate result.
Envelopes, much like Bollinger Bands are a way of seeing potential movement zones along with potential Support and Resistance. However, unlike Bollinger Bands which are based on Standard Deviation, Envelopes are based on percentages +/- from the Simple Moving Average.
We will conclude our Tutorial here. Hopefully this has given you some insight into how useful adding a ‘Optimal Length’ within an external (secondary) Indicator as a Source within the Settings may be. Likewise, how useful it may be for automation sake in the sense that when the ‘Optimal Length’ changes, it doesn’t rely on an alert where you need to manually update it yourself; instead it will update Automatically and you may reap the benefits of such with little manual input needed (aside from the initial setup).
If you have any questions, comments, ideas or concerns please don't hesitate to contact us.
HAPPY TRADING!

Adaptive-Lookback Stochastic [Loxx]Adaptive-Lookback Stochastic is an adaptive stochastic indicator.
The Adaptive lookback is truly a market-driven period input used to determine the variable lookback period for many different indicators, instead of a traditional, fixed figure.
It is based on the frequency of market swings - the time between swing highs or swing lows. A swing high is defined as two consecutive higher highs followed by two consecutive lower highs; a swing low is defined by two consecutive lower lows followed by two consecutive higher lows. As swing points typically accompany reversals, they occur more frequently in choppier and volatile markets than in trends.
Adaptive lookback period is determined as :
Determine the initial number of swing points (swing count parameter) to use in the calculation.
Count the number of price bars it takes for the n swing points to form.
Divide step 2 by step 1 and round the result.
As an addition, adjust the "speed" of the produced period using the speed parameter - the smaller the speed parameter, the "slower" the average, and vice versa
Included
Bar coloring
Loxx Expanded Source Types
3 types of signals: levels crosses, slope, and middle crosses
Alerts

Adaptive-Lookback CCI w/ Double Juirk Smoothing [Loxx]Adaptive-Lookback CCI w/ Double Juirk Smoothing is a CCI indicator with Adaptive period inputs. The adaptive calculation in this case is the count of pivots in historical bars. This indicator is also double smoothing using Jurik smoothing to reduce noise and refine the signal.
What is CCI?
The Commodity Channel Index ( CCI ) measures the current price level relative to an average price level over a given period of time. CCI is relatively high when prices are far above their average. CCI is relatively low when prices are far below their average. Using this method, CCI can be used to identify overbought and oversold levels.
What is Jurik Volty used in the Juirk Filter?
One of the lesser known qualities of Juirk smoothing is that the Jurik smoothing process is adaptive. "Jurik Volty" (a sort of market volatility ) is what makes Jurik smoothing adaptive. The Jurik Volty calculation can be used as both a standalone indicator and to smooth other indicators that you wish to make adaptive.
What is the Jurik Moving Average?
Have you noticed how moving averages add some lag (delay) to your signals? ... especially when price gaps up or down in a big move, and you are waiting for your moving average to catch up? Wait no more! JMA eliminates this problem forever and gives you the best of both worlds: low lag and smooth lines.
Included:
Bar coloring
3 signal variations w/ alerts

True Adaptive-Lookback Phase Change Index [Loxx]Previously I posted a Phase Change Index using Ehlers Autocorrelation Periodogram Algorithm to tease out the adaptive periods. You can find the previous version here: . This new version is also adaptive but uses a different method to derive the adaptive length inputs. This adaptive method derives period inputs by counting pivots from past candles. This version also relies on Jurik Smoothing to generate the final signal. I named this one "true" because I should have specified in the previous PCI's title that it's powered by Ehlers Autocorrelation Periodogram. Additionally, you'll notice the ALB algorithm has changed from other indicators, This is restrict the range of possible ALB period outputs to a specific range so the indicator is usable.
And remember, this is an inverse indicator. This means that small values on the oscillator indicate bullish sentiment and higher values on the oscillator indicate bearish sentiment.
What is the Phase Change Index?
Based on the M.H. Pee's TASC article "Phase Change Index".
Prices at any time can be up, down, or unchanged. A period where market prices remain relatively unchanged is referred to as a consolidation. A period that witnesses relatively higher prices is referred to as an uptrend, while a period of relatively lower prices is called a downtrend.
The Phase Change Index ( PCI ) is an indicator designed specifically to detect changes in market phases.
This indicator is made as he describes it with one deviation: if we follow his formula to the letter then the "trend" is inverted to the actual market trend. Because of that an option to display inverted (and more logical) values is added.
What is the Jurik Moving Average?
Have you noticed how moving averages add some lag (delay) to your signals? ... especially when price gaps up or down in a big move, and you are waiting for your moving average to catch up? Wait no more! JMA eliminates this problem forever and gives you the best of both worlds: low lag and smooth lines.
Ideally, you would like a filtered signal to be both smooth and lag-free. Lag causes delays in your trades, and increasing lag in your indicators typically result in lower profits. In other words, late comers get what's left on the table after the feast has already begun.
That's why investors, banks and institutions worldwide ask for the Jurik Research Moving Average ( JMA ). You may apply it just as you would any other popular moving average. However, JMA's improved timing and smoothness will astound you.
What is adaptive Jurik volatility
One of the lesser known qualities of Juirk smoothing is that the Jurik smoothing process is adaptive. "Jurik Volty" (a sort of market volatility ) is what makes Jurik smoothing adaptive. The Jurik Volty calculation can be used as both a standalone indicator and to smooth other indicators that you wish to make adaptive.
Included:
Bar coloring
2 signal variations w/ alerts

Variety RSI of Adaptive Lookback Averages [Loxx]Variety RSI of Adaptive Lookback Averages uses an adaptive lookback algorithm in order to determine dynamic length inputs to get used to smooth the input price source before calculating your choice of 6 different types of RSI. This ALB algorithm counts bars back until X many swing counts are reached.
Included:
Bar coloring
2 signal variations w/ alerts