John Ehlers, the developer of MESA, has written and published many papers relating to the principles used in market cycles. Synopses for the papers available are displayed below. Download each by selecting their associated HyperText.
Walk Forward Optimization
It is common knowledge that simple backtesting can provide a poor probability of future trading results. A better indicator of future performance can be done through Walk Forward Optimization (WFO), where out of sample testing is done a little at a time. However WFO testing is not without its own problems. This paper describes how to get reliable results.
A Procedure to Evaluate Trading Strategy Robustness
This paper describes a unique way to visualize the potential robustness of a trading strategy in the TradeStation or Multicharts platforms. The procedure includes a way to identify the optimization range of input parameters.
Why Traders Lose Money (and What to Do About It)
An article in the May 2014 issue of Stock & Commodities Magazine described how to create artificial equity curves by just knowing the Profit Factor and Percent Winners of a Trading Strategy. Bell Curve statistics for trading randomly selected stocks and portfolio trading are also included. This is an Excel Spreadsheet that enables you to experience these statistical descriptors of trading system performance.
Predictive Indicators for Effective Trading Strategies
Technical traders understand that indicators need to smooth market data to be useful, and that smoothing introduces lag as an unwanted side-effect. We also know that the market is fractal; a weekly interval chart looks just like a monthly, daily, or intraday chart. What may not be quite as obvious is that as the time interval along the x-axis increases, the high-to-low price swings along the y-axis also increase, roughly in proportion. This "spectral dilatation" phenomena causes an undesirable distortion, one that has either not been recognized or has been largely ignored by indicator developers and market technicians.
Inferring Trading Strategies from Measured Probability Density Functions
This was the Runner-up Winner of the MTA's 2008 Charles H. Dow Award. In this paper I show the implications of the various forms of detrending and how the resultant Probability Distributions can be used as strategies to generate effective trading systems. Results of these robust trading systems are compared to standard approaches.
This paper show and interactive way to eliminate as much lag as desired from smoothing filters. Of course, reduced lag comes at the price of decreased filter smoothness. The filter exhibits no transient overshoot commonly found in higher order filters.Zero Lag , download 335Kb
Empirical Mode Decomposition
A novel approach for cycle and trend mode detection.
Fourier Transform for Traders
The problem with Fourier Transform for the measurement of market cycles is that they have a very poor resolution. In this paper I show how to use another nonlinear transform to improve the resolution so that the Fourier Transforms are usable. The measured spectrum is displayed as a heatmap
Swiss Army Knife Indicator
Indicators are just transfer responses of input data. By a simple change of constants, this indicator can become an EMA, SMA, 2 Pole Gaussian Low Pass Filter, 2 Pole Butterworth Low Pass Filter, an FIR smoother, a Bandpass filter, or a Bandstop filter.
An unusual nonlinear FIR filter is described. This filter is among the most responsive to price changes but smoothest in sideways markets.
System Performance Evaluation
Profit Factor (gross winnings divided by gross losses) is analogous to the payout factor in gaming. Thus, when the Profit Factor is combined with the percentage winners in a series of random events, instances of how a trading strategy equity growth can be simulated. This paper describes how common performance descriptors are related to these two parameters. An Excel spreadsheet is described, allowing you to perform a Monte Carlo Analysis of your trading systems if you know these two parameters (out of sample).
FRAMA (FRactal Adaptive Moving Average). A nonlinear moving average is derived using the Hurst exponent.
MAMA is the mother of all adaptive moving averages. Actualy the name is an acronym for MESA Adaptive Moving Average. The nonlinear action of this filter is produced by the flyback of phase every half cycle. When combined with FAMA, a Following Adaptive Moving Average, the crossovers form excellent entry and exit signals that are relative free of whipsaws.
Time Warp Without Space Travel
Laguerre Polynomials are used to generate a filter structure similar to a simple moving average with the difference that the time spacing between filter taps is nolinear. The result enables the creation of very short filters having the smoothing characteristics of much longer filters. Shorter filters mean less lag. The advantages of using the Laguerre Polynomials in filters is demonstrated in both indicators and automatic trading systems. The article includes EasyLanguage code.
The CG Oscillator
The CG Oscillator is unique because it is an oscillator that is both smoothed and has zero lag. It finds the Center of Gravity (CG) of the price values in an FIR filter. The CG automatically has the smoothing of the FIR filter (similar to a simple moving average) with the position of the CG being exactly in phase with the price movement. EasyLanguage code is included.
Using the Fisher Transform
Many trading systems are designed using the assumption that the probability distribution of prices have a Normal, or Gaussian, Probability Distribution about the mean. In fact, nothing could be farther from the truth. This paper describes how the Fisher Transform converts data to have nearly a Normal Probability Distribution. Given the Probability Distribution is Normal after applying the Fisher Transform, the data is used to create entry points with surgical precision. The article includes EasyLanguage code.
The Inverse Fisher Transform
The Inverse Fisher Transform can be used to generate an oscillator that switches quickly between oversold and overbought without whipsaws.
Lag is the downfall of smoothing filters. This article shows how lag can be reduced and the highest fidelity smoothing is obtained by reducing the lag of high frequency components in the data. A complete table of Gaussian filter coefficients is provided.
Poles and Zeros
A description of digital filters in terms of Z Transforms. The ramifications of higher order filters are described. Tables of coefficients for 2 Pole and 2 Pole Butterworth filters are given.