Profitable Moving Average Crossover

Hi everyone!

Introduction
A popular use for moving averages is to develop simple trading systems based on moving average crossovers. A trading system using two moving averages would give a buy signal when the shorter (faster) moving average advances above the longer (slower) moving average. A sell signal would be given when the shorter moving average crosses below the longer moving average. The speed of the systems and the number of signals generated will depend on the length of the moving averages.

There are many types of averages that are based on different techniques. Each type has its drawbacks and merits. And if we decide to choose a certain type of average for the trading system, then how do we know that our choice is optimal?

What is this tool?
This tool will help you to choose this type to create the most profitable trading system based on crossovers for the specified periods. It backtests pairs of each type throughout the whole instrument's history and shows Net Profit curves as a result. So, the type of the most profitable crossover system will be at the top of list of labels on the chart. (Click on the price scale, point to "Labels" and switch off "No Overlapping Labels" option).

Settings
The main settings are periods for each type pair of fast and slow moving averages.
Additionally, it allows to customize some multi-parametric moving averages such as JMA, ALMA, McGinley Dynamic, Adaptive Laguerre Filter etc.

• 1st Period (default: 14)
  
• 2nd Period (default: 50)
  
• 1st ALF Median Length (default: 5)
  
• 2nd ALF Median Length (default: 5)
  
• 1st ALMA Offset (default: 0.85)
  
• 1st ALMA Sigma (default: 6)
  
• 2nd ALMA Offset (default: 0.85)
  
• 2nd ALMA Sigma (default: 6)
  
• 1st HF Scaling Factor (default: 3)
  
• 2nd HF Scaling Factor (default: 3)
  
• 1st JMA Phase (default: 50)
  
• 2nd JMA Phase (default: 50)
  
• 1st MD Constant (default: 0.6)
  
• 2nd MD Constant (default: 0.6)
  
• 1st MHLMA Range (default: 10)
  
• 2nd MHLMA Range (default: 10)
  
• 1st PWMA Power (default: 2)
  
• 2nd PWMA Power (default: 2)
  
• 1st REMA Lambda (default: 0.5)
  
• 2nd REMA Lambda (default: 0.5)
  
• 1st RMF Median Length (default: 5)
  
• 2nd RMF Median Length (default: 5)
  
• 1st T3 Alpha (default: 0.7)
  
• 2nd T3 Alpha (default: 0.7)
  
• MAMA & FAMA Fast Limit (default: 0.5)
  
• MAMA & FAMA Slow Limit (default: 0.05)
  

Supported types of averages and filters (use short titles to match averages on the chart)

• AHMA, Ahrens MA (by Richard D. Ahrens)
  
• ALMA, Arnaud Legoux MA (by Arnaud Legoux and Dimitris Kouzis-Loukas)
  
• ALF, Adaptive Laguerre Filter (by John F. Ehlers)
  
• ARSI, Adaptive RSI
  
• BF2, Butterworth Filter with 2 poles
  
• BF3, Butterworth Filter with 3 poles
  
• DEMA, Double Exponential MA (by Patrick G. Mulloy)
  
• DWMA, Double Weighted (Linear) MA
  
• EDCF, Ehlers Distance Coefficient Filter (by John F. Ehlers)
  
• EHMA, Exponential Hull MA
  
• EMA, Exponential MA
  
• EVWMA, Elastic Volume Weighted MA (by Christian P. Fries)
  
• FRAMA, Fractal Adaptive MA (by John F. Ehlers)
  
• GF1, Gaussian Filter with 1 pole
  
• GF2, Gaussian Filter with 2 poles
  
• GF3, Gaussian Filter with 3 poles
  
• GF4, Gaussian Filter with 4 poles
  
• HFSMA, Hampel Filter on Simple Moving Average
  
• HFEMA, Hampel Filter on Exponential Moving Average
  
• HMA, Hull MA (by Alan Hull)
  
• HWMA, Henderson Weighted MA (by Robert Henderson)
  
• IDWMA, Inverse Distance Weighted MA
  
• IIRF, Infinite Impulse Response Filter (by John F. Ehlers)
  
• JMA, Jurik MA (by Mark Jurik,
  
  )
  
• LF, Laguerre Filter (by John F. Ehlers)
  
• LMA, Leo MA (by ProRealCode' user Leo)
  
• LSMA, Least Squares MA (Moving Linear Regression)
  
• MAMA & FAMA, (by John F. Ehlers, special case that used as a benchmark)
  
• MD, McGinley Dynamic (by John R. McGinley)
  
• MHLMA, Middle-High-Low MA (by Vitali Apirine)
  
• PWMA, Parabolic Weighted MA
  
• REMA, Regularized Exponential MA (by Chris Satchwell)
  
• RMA, Running MA (by J. Welles Wilder)
  
• RMF, Recursive Median Filter (by John F. Ehlers)
  
• RMTA, Recursive Moving Trend Average (by Dennis Meyers)
  
• SHMMA, Sharp Modified MA (by Joe Sharp)
  
• SMA, Simple MA
  
• SSF2, Super Smoother Filter with 2 poles (by John F. Ehlers)
  
• SSF3, Super Smoother Filter with 3 poles (by John F. Ehlers)
  
• SWMA, Sine Weighted MA
  
• TEMA, Triple Exponential MA (by Patrick G. Mulloy)
  
• TMA, Triangular MA (generalized by John F. Ehlers)
  
• T3, (by Tim Tillson)
  
• VIDYA, Variable Index Dynamic Average (by Tushar S. Chande)
  
• VWMA, Volume Weighted MA (by Buff P. Dormeier)
  
• WMA, Weighted (Linear) MA
  
• ZLEMA, Zero Lag Exponential MA (by John F. Ehlers and Ric Way)
  

NOTE: The results may vary on different tickers and timeframes.
If you see the preview result it doesn't mean that these crossovers will be profitable on other instruments and timeframes. This is a normal situation because time series and their characteristics differ.
I know that because I tested this tool before publishing.

NOTE 2: You can use this tool by yourself and experiment with it, or you can order a study and I will share the spreadsheet that contains results with you.

Good luck!

Release Notes:

• Now it uses "Early Switch" version of the algorithm
  
• Added an alert to notify when the most profitable crossover type changed
  
• Made minor optimizations
  

Release Notes:

• Fixed bug with periods <= 2
  
• Added new moving averages
  
• SHMMA (Sharp Modified Moving Average) was removed due to too much similarity to LSMA
  

New Moving Averages:

• AEMA, Adaptive Exponential MA (by Vitali Apirine)
  
• AMA, Adaptive MA (by Vitali Apirine)
  
• BAMA, Bryant Adaptive MA (by Michael R. Bryant)
  
• EDSMA, Ehlers Deviation-Scaled MA (by John F. Ehlers)
  
• JAMA, Jurik Adaptive MA (by Mark Jurik)
  
• KAMA, Kaufman Adaptive MA (by Perry J. Kaufman)
  
• MNMA, McNicholl MA (by Dennis McNicholl)
  
• NSMA, Moving Average 3.0 on SMA (by Manfred G. Dürschner)
  
• NEMA, Moving Average 3.0 on EMA (by Manfred G. Dürschner)
  
• NWMA, Moving Average 3.0 on WMA (by Manfred G. Dürschner)
  
• NVWMA, Moving Average 3.0 on VWMA (by Manfred G. Dürschner)
  
• PEMA, Pentuple Exponential MA (by Bruno Pio)
  
• QMA, Quick MA (by John McCormick)
  
• QEMA, Quadruple Exponential MA (by Bruno Pio)
  

The total number of MA crossovers on test is 60 now

Release Notes:

• Security update
  

Release Notes:

• Security update
  

Release Notes:

• Security update
  

Release Notes:

• Added optimization fixes
  
• Security update
  

Release Notes:

• Update
  

Release Notes:

• Update
  

Release Notes:

• Update
  

Release Notes:

• Bump Pine Script version to 4