Meyers

Analytics

Analytics

Advanced Mathematical Trading Strategies & Walk Forward Out-Of-Sample Analysis

applied to algorithmic trading of stocks, futures & forex

Info: (312) 280-1687 support@meyersanalytics.com

applied to algorithmic trading of stocks, futures & forex

Info: (312) 280-1687 support@meyersanalytics.com

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Power Walk Forward

Optimizer Walk Forward

Metric Explorer Walk Forward

Input Explorer Walk Forward

Surface Explorer Key Daily & Intraday

Trading Strategies Nth Order Fixed Memory

Polynomial Strategy Nth Order Fading Memory

Polynomial Strategy End Point Fast Fourier

Transform Strategy Goertzel DFT

Strategy Five Parameter

Parabolic Strategy Dennis Meyers

Working Papers

Optimizer Walk Forward

Metric Explorer Walk Forward

Input Explorer Walk Forward

Surface Explorer Key Daily & Intraday

Trading Strategies Nth Order Fixed Memory

Polynomial Strategy Nth Order Fading Memory

Polynomial Strategy End Point Fast Fourier

Transform Strategy Goertzel DFT

Strategy Five Parameter

Parabolic Strategy Dennis Meyers

Working Papers

Recently (1980's), interest has developed in what are called robust regression and outlier detection techniques, Ref [1]. Regression techniques are now defined by a measure called the "breakdown point". The breakdown point is loosely defined as the smallest amount of bad data points that can cause the regression solutions to take on values arbitrarily far from their true values. Unfortunately the Least Squares technique has a breakdown point of 1/N. In other words only one bad data point can significantly change the computation of the velocity or slope of a straight line. The median of a set of numbers has a breakdown point of 50% . This is because when 50% of the numbers are bad then there is no way of telling which are the bad numbers and which are the good numbers. 50% is the highest breakdown point.

Recently Siegel Ref[2], in his paper "Robust regression using repeated medians", introduced a technique for finding the slope that has a 50% breakdown point. The repeated median is also described in Ref [1].

The mathematical formula for the Repeated Median is:

Slope(t) =median_{ i (i=1 to N)} {median_{ i≠j (j=1 to N)} [(price(j)-price(i))/(j-i)] }

The repeated median slope is used to create a system. For a straight line the velocity is equal to the slope. The repeated median velocity has the advantage that it is a natural random price noise inhibitor. We can create a system such that unless the repeated median velocity using N past price bars is greater than some threshold we will not buy or sell. A large percentage of price noise generates a lot of back and forth movements of small magnitudes over a short period of time. With a lot of systems this back and forth movement creates many false buy and sell signals. However using the repeated median velocity over N past prices, we can filter out many of the small price noise movements by requiring that the velocity to be greater than some threshold before we act.

References

- Rousseeuw, P.J., Leroy, A.M., (1987) "Robust Regression and Outlier Detection", New York, John Wiley & Sons.
- Siegel, A.F. (1982), "Robust Regression using Repeated Medians." Biometrika. 69, pp242-244.

The Repeated Median Velocity System Input Parameters

**N**= The number of prices used in the calculation of the Repeated Median Velocity.**vup**= The threshold amount that Repeated Median Velocity has to be greater than to issue a buy signal.**vdn**= The threshold amount that Repeated Median Velocity has to be less than to issue a sell signal.**XOpn**= Used only for Intraday bars. Prevents buys or sells until XOpn bars have past since the open. 0 = Ignore. Note, this input parameter avoids many opening gap whipsaws.**Xtime**, = Used only for Intraday bars. Exit position before or at the close. If XTime= 1610 then exit at 4:10pm EST. 0 = ignore

My working paper on the **Robust Repeated Median Velocity System ** can be found on the Papers Page

**Product Description **

The Robust Repeated Median Velocity system is orientated to short term trading in all bar ranges (1 tic, 1 min, 5min, etc., daily) and with any tradeable price series. This system can also be used on futures, stocks, options, and mutual fund data.

For **TradeStation, Multicharts** all of the EasyLanguageâ„¢ strategy and indicator codes are directly importable into your choice of TS9 or MC and are ** fully disclosed.** There are

For **NeuroShell Trader/DayTrader Pro,** the Trading Strategy and Indicators are directly imported into NeuroShell via a special setup exe file and are fully disclosed in the Indicator wizard "MA_KeyTrSys" category and in the Trading Strategy Wizard "MA_KeyTrSys" directory. The C++ DLL code is not disclosed. The Input parameters to the strategy and indicator are changeable and optimizable so that the user can develop his own parameter set on his price series and time frame of interest. Although the system results will give parameters for the intraday or daily futures the system was tested on, the user can easily use this system on any tradeable or on any time frame.

The ** accompanying page manual** consists of:

**A short tutorial on the details of performing walk forward optimization with out-of-sample testing using TradeStation and how I look for the "best" parameters in a TS combinatorial optimization run(available in the TS Manual only).****A complete description of the Robust Repeated Median Velocity system, it's derivation and it's input parameters.****The walk forward optimization method used and a table of the walk forward results for the system.****The input parameter test ranges****How to setup a chart using the Strategies and Indicators in TradeStation or NeuroShell**.**An EasyLanguage Strategy and Indicator code printout (TradeStation only)****A chart printout with the Strategy and it's associated Indicator with all the system buy and sell signals displayed on the chart.****Performance Summaries for the test period and the out-of sample period segments.****Special %Runup-%Drawdown for each trade, trade by trade Summaries.**

In addition The Robust Repeated Median Velocity system has its exact duplicate in indicator form which is displayable on the price chart, so that the user can visually see how the buy and sell signals occur.

For **TradeStation, MultiCharts The Robust Repeated Median Velocity System™** is one of the 6 systems included in the Key Daily &Intraday Trading Systems package. The Key Daily &Intraday Trading Systems package is being offered through

For **NeuroShell Trader/DayTrader Pro,** ** The Robust Repeated Median Velocity System™ ** is one of the 6 systems included in the Key Daily &Intraday Trading Systems package.. The Key Daily &Intraday Trading Systems package is being offered through

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Thank you for your Interest....Dennis Meyers