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

Order Online
Power Walk Forward

Optimizer Walk Forward

Performance Explorer 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

Performance Explorer 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

Videos On How To Use The PWFO

The Power Walk Forward Optimizer (PWFO) is a cutting-edge automatic walk forward testing program that eliminates the ad hoc curve fitting produced by optimization of strategy input values on spurious price movements. This package contains a walk forward optimization add-on program that can be added to any TS or MC strategy using TS or MC multiple strategy option. The PWFO prints out the in-sample performance ** and the out-of-sample performance results**, on one line, for each input variable combination that is run by the TradeStation(TS) optimization module to a user selected spreadsheet comma delimited file. The PWFO can generate up to 500 different in-sample and out-of-sample date optimization files in one optimization run saving the user from having to generate optimization runs one at a time. It is not well know but statistically speaking, walk forward out-of-sample (oos) analysis must be performed over many(>30) in-sample/oos sections to be statistically valid. The PWFO output allows you to quickly determine whether your procedure for selecting input parameters for your strategy just curve fits the price and noise or produces statistically valid out-of-sample results.

In addition to the out-of-sample performance results presented for each case, 30+ superior and robust performance metrics (many are new and never presented before) are added to each case line and printed out to the comma delimited file. ** The PWFO also allows the user to code up to five of their own performance metrics in EasyLanguage which is then included with the PWFO performance metrics on each case line. **

Out-of-sample testing is the norm in all mathematical economic disciplines other than technical analysis. The basis of walk forward out-of-sample testing is to take a test sample (in-sample) of data, perform a combinatorial input parameter search (dubbed optimization by current trading platforms) on the in-sample data, choose the input parameters from the combinatorial search based upon some performance metric (net profit, profit factor, etc) in the in-sample sample and then apply the input parameters to data they haven't been tested on to see if they work.

Why use walk forward analysis? Why not just optimize over the total amount of data once and choose the inputs from the best performance parameters? Optimization is a misnomer and should really be called Combinatorial search

. That is, we have the software output certain performance metrics like net profit or profit factor for every combination of a range of input parameters. We then sort that range on that performance metric. Whenever you run an combinatorial or genetic search over many different combinations of input parameters on noisy data on a fixed time interval, the best performance parameters found are guaranteed be due to “curve fitting” the noise and signal. This curve fitting is also called Data Mining

or Data Snooping

. A fixed number of prices on a fixed time interval has many spurious movements which is also called noise. When we run, say, 5000 different input variations or cases, the best performance parameters will be from those system input variables that are able to produce profits from the price or signal dynamics ** and** the spurious movements . While the signal dynamics,

cherry pickedto perform well on only those exact same spurious movements. This is why combinatorial or genetic searches with no out-of-sample testing cause loses in the out-of-sample section from something that looked great in the in-sample section.

The PWFO can print up to 500 in-sample and out-of-sample(OOS) files in just one TS optimization run. The in-sample and out-of-sample periods are user selectable in days or exact calendar months. For instance, in this necessarily short example, suppose we had one minute bar data from 4/12/10 to 6/4/10 loaded into a TS chart with a strategy combined with the PWFO. If we set the PWFO to calculate a in-sample period of 28 calendar days (4 weeks) and an OOS period of 7 calendar days (1 week) of 1 minute bar price data, the PWFO would generate the following four in-sample-OOS output files for each case of the strategy's optimization run assuming there was no price data on the weekends:

- File1 - in-sample Dates 4/12 to 5/07 OOS Dates 5/10 to 5/14 (5/08,5/09 = weekend)
- File2 - in-sample Dates 4/19 to 5/14 OOS Dates 5/17 to 5/21 (5/15,5/16 = weekend)
- File3 - in-sample Dates 4/26 to 5/21 OOS Dates 5/24 to 5/28 (5/22,5/23 = weekend)
- File4 - in-sample Dates 5/03 to 5/28 OOS Dates 5/31 to 6/04 (5/29,5/30 = weekend)

- File1 - in-sample Dates 12/1/09 to 3/31/10 OOS Dates 4/1/10 to 4/30/10
- File2 - in-sample Dates 1/1/10 to 4/30/10 OOS Dates 5/1/10 to 5/31/10
- File3 - in-sample Dates 2/1/10 to 5/31/10 OOS Dates 6/1/10 to 6/30/10
- File4 - in-sample Dates 3/1/10 to 6/30/10 OOS Dates 7/1/10 to 7/31/10

If the optimization run consisted of 5000 different cases of the strategy input variables, then each of the PWFO files would have 5000 lines and each PWFO file would represent only the in-sample-oos performance for the indicated dates. Of course if the data loaded into TS was much longer in time, then the PWFO could generate up to 500 different sample in-sample-oos date files.

For each TS run, the user can select the in-sample dates he wants to perform the optimization on and the out-of-sample(OOS) dates for out-of-sample performance. The in-sample and out-of-sample periods are user selectable in calendar days or exact calendar months. After examining fifty or more different in-sample and out-of-sample files, the user rapidly gets a real feel for the statistics and filters that are important for determining good out-of-sample performance. No more guess work. The PWFO is a real time saver. Please note that the median is used for a number of performance statistics instead of the average. The median is a much more robust measure than the average and is not distorted by outliers.

Below are the performance metrics that are printed out for each input variable case.

*in-sample Data Performance Metrics***Input Variables****Total Net Profits of All Trades in Test(In-Sample) Section (tnp)****The Median of All Trades in the Test(In-Sample) Section (mTrd)****Number of Trades (nT)****Percent Profitable Trades (%P)****Profit Factor (PF)****Standard Deviation of Trades(std)****Student t-statistic. Used to determine the probability that the Ave Trade Profit is > 0 (t)****The Median of Bars in Losing Trades (mLBr)****Total Losing Bars (tLBr)****The Median of Bars in Winning Trades (mWBr)****Total Winning Bars (tWBr)****Ratio of Median Winning Bars to Median Losing Bars (mWB|LB)****Ratio of Total Winning Bars to Total Losing Bars (tWB|LB)****Median of all Trades{Maximum Trade Runup minus Final Trade Profit} (m(RU-p))****Median of all Trades{Final Trade Profit minus Maximum Trade Rundown) (m(p-RD))****Maximum Consecutive Winners In-A-Row (wr)****Maximum Consecutive Losers In-A-Row (lr)****Median Of The Winning Trades (mWTrd)****Median Of The Losing Trades (mLTrd)****Ratio of Median Winning Trades /Median Losing Trades (mWT|LT)****Maximum Drawdown (dd)****Largest Losing Trade (llt)****Slope of Trade Equity Regression Line (eqTrn)****Trade Equity Regression Trend Line Coefficient of Correlation R**^{2}(eqR2)**Median of The Deviation between the absolute Values of Each Trade Equity Minus The Equity Regression Trend Line (eqDev)****Slope of Trade Equity Least Squares 2nd Order Polynomial Line where Equity=b**_{0}+ b_{1}*i + b_{2}*i^{2}(eq2B1)**Velocity of Equity Curve Least Squares 2nd Order Polynomial Line.(eq2V)****Acceleration of Equity Curve Least Squares 2nd Order Polynomial Line. (eq2A)****Equity Least Squares 2nd Order Polynomial Line Coefficient of Correlation R**^{2}(eq2R2)**Projected Equity 10 Trades In Future Using Equity Curve Least Squares 2nd Order Polynomial Line.(eq10)****Modified K-ratio = Slope of Equity Regression Line/ (The Average of The Absolute Values of The Equity at Each Trade Minus The Equity Regression Trend Line). (mKr)****User Performance Metric = The user codes their own performance metric in EasyLanguage and this metric is include with the output. (um)**

*Out-Of-Sample Data Performance Statistics***Out-Of-Sample Net Profit (osnp)****Out-Of-Sample Drawdown (odd)****Out-Of-Sample Largest Losing Trade (ollt)****Out-Of-Sample Number Of Trades (ont)****Out-Of-Sample Average trade Profit (aoTrd)**

Below is a snippet of the output from a PWFO run. This example shows the partial output for the Goertzel Strategy for the in-sample dates of 7/26/12 to 8/24/12 and out-of-sample dates of 8/27/12 to 8/31/12. Notice how the out-of-sample results are on the same line as the input parameters and in-sample performance variables. This output presentation allows you to see immediately the out-of-sample results from your in-sample performance variable selection techniques. For instance if you wanted to see all those cases that satisfied a Profit Factor greater than 1 and less than 3 with losers in a row of 3 or less, then using Excel's Autofilter feature, you could immediately see all cases that satisfied those criteria and what the out-of-sample results would be. In addition, using Excel's macro creation ability you can create an excel macro to perform your own performance variable screen with a one button click. This allows you to go through the many walk forward files created by the PWFO in minimal time to see how your performance variable screen or filter works over many in-sample/out-of-sample runs. The Walk Forward Performance Explorer, The Walk forward Metric Explorer and the Walk Forward Metric Surface Explorer perform these filter searches automatically. As noted above, the PWFO uses the median instead of the average whenever we can. The median is a much more robust statistic than the average. As an example look at row 3 on the below spreadsheet snippet. The median trade profit is minus **-$260** while the average trade profit (tnp/nT) is a plus **$52**. The average is controlled by a few outliers while the median is robust and immune to these few outliers.

**How is the use of the PWFO possible with any Strategy?** TradeStation TS9's strategy combining window allows for the combining of any number of strategies or signals into one strategy. The PWFO is a strategy that computes and prints out to a user defined directory and Excel file all the performance statistics above using a super fast C++ DLL. For TS9 or MultiCharts you need to access the Power Editor for your strategy and add the line value99=$PWFOinp(input1,input2,input3,etc); at the end of "YourStrategy". Then, do a "save as" with a new name like "YourStrategyPWFO", and you are ready to use the PWFO.

**The Power Walk Forward Optimizer comes with a detailed manual explaining:**

- How to setup a TS9 with the PWFO and any strategy/signal
- How to use the PWFO with any strategy.
- An explanation of each of the performance statistics.
- How to enter and code your user performance metric in easy language.
- How to use the generated optimization Excel output file.
- Walk Forward Optimization tutorial.
- PWFO TS9 EasyLanguage code (C++ DLL code not included).

**User Comparison between TS Walk Forward optimizer (Grail) and the PWFO ** "The pwfo brought about a deeper understanding of how to properly optimize a system. There are things I learned though that process that I now incorporate into my new strategy development. Even though it was a difficult process, I finished a much wiser system designer. So for me the steep pwfo learning curve was ultimately an advantage. The biggest difference from the grail is that pwfo includes a methodology on how to properly evaluate trading systems. That is not available anywhere else. I spent 6 months using the Grail, prior to encountering the pwfo, optimizing while not being fully aware that I didn't know how to properly interpret my results and guide my decisions in a more consistently and profitable way. This resulted in all my systems not conforming to my back test results in real time.
The next difference in systems is a huge improvement as well. Using metric filters to arrive at my final trading input variables is not discussed or possible with the grail and I think the pwfo method is superior. Further more the best way to optimize in pwfo is to give up profit and explore metrics/variables that reside in the median values. That is not discussed or possible with the grail.
A typical grail optimization will take me a few hours. A typical pwfo optimization requires at least 4 full optimization runs and a lot of thinking and comparing so this process requires a minimum of 1 day and often many days.
There are fewer statistics in a grail optimization run and it is not currently possible to export All the results from grail to an excel spreadsheet for further analysis. There is an export function in Grail but it will not export all the variables or the walk forward tests, only 1 final optimized test result. So I am forced in Grail to view the results inside TradeStation."

** Compatibility Note: **It is possible to use the PWFO with

For TradeStation TS9 or MultiCharts, the ** Power Walk Forward Optimizer v3** package consisting of manual, DLL files and TradeStation ELD file is being offered, for

To order online

Thank you for your Interest....Dennis Meyers