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Dennis Meyers
Working Papers
The Adaptive N Cycle Goertzel Discrete Fourier Transform (nCycleGZ) System for short term & intraday trading This package contains the advanced mathematical technique called the Goertzel algorithm for discrete Fourier transforms. This mathematical technique is currently used in today's space-age satellite and communication applications and is applied here to stock and futures trading.

While the mathematical technique called the Goertzel algorithm is unknown to many, this algorithm is used everyday without even knowing it. When you press a cell phone button have you ever wondered how the telephone company knows what button tone you pushed? The answer is the Goertzel algorithm. This algorithm is built into tiny integrated circuits and immediately detects which of the 12 button tones(frequencies) you pushed. Here we will use the Goertzel algorithm to detect the frequencies of price series.

In a my working paper entitled "MESA vs Goertzel DFT" (papers page) , I demonstrated that the Goertzel-DFT Algorithm has superior frequency detection abilities for sine waves imbedded in noise when compared to the MESA algorithm. Previous researchers using MESA constrained themselves to using MESA to find only the cycle with the highest amplitude and called that cycle the dominant cycle. In this system, we will find and use the frequencies with the N (N is user selectable from 1 to 10) highest amplitudes to create a noise filtered signal curve that we will follow to create our system buy and sell signals. The Adaptive N Cycle Goertzel Discrete Fourier Transform (nCycleGZ) super fast DLL finds the N cycles(frequencies) with the highest amplitudes at each price bar, and creates a x bar ahead(x is user selectable) noise filtered projected momentum curve. This process gives a more robust noise filtered signal than a single frequency (dominant cycle) procedure. You are no longer constrained to using only a single frequency. The nCycleGZ algorithm is faster and superior to MESA in finding cycles in noisy price series.

The Adaptive N Cycle Goertzel-DFT System.(See working paper entitled "The Adaptive 10 Cycle Goertzel-DFT System" on papers page)
The nature of intraday price movements is constantly changing due to current economic surprises, events and trader sentiment. Also, the time of year changes the nature of intraday markets, such as the seasons, holidays, vacation time, etc. As such, the periods or frequencies found on intraday prices three months ago may no longer be the same as the frequencies found on today's intraday data. We expect the frequencies found on intraday data to vary over time.

For this system we create a strategy that walks forward one bar at a time. The strategy will take a fixed number, M, of closing prices and use the Goertzel Algorithm(GA) to find the N frequencies with the highest amplitudes. Using those N frequencies, amplitudes and phases, we will construct a new price that forecasts the price x bars ahead. We will save this x bar forecast value, or forecast point. Next, we move the M closing prices forward one bar adding the next bar and dropping the last bar so that we have exactly M closing prices again. With this new M closing prices window, we compute the next bar forecast value from the N frequencies found by the GA and save it. We keep marching the M closing price window forward one bar at a time, calculate and save the new forecast point until we reach the end of our data. We then connect all the generated forecast points to produce a curve that creates the N cycle next x bar forecast as the N frequencies used to create the next x bar forecast change over time. Thus, this curve adapts to the closing price's changing frequencies and projects x bars ahead so that it's lag is minimized when things change.

The nCycleGZ system is orientated to short term trading in all bar ranges (1 min, 5min, etc., daily) and with any tradeable price series. The Input parameters to the system 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 nCycleGZ system gives results for the parameters that the E-Mini future was tested on, the user can easily use the system on any future or stock or on any time frame.

For TradeStation

All of the EasyLanguage™ strategy and indicator codes are directly importable into your choice of TS2000i or TS8 and are fully disclosed. There are no locks of any kind on the EasyLanguage source code. The C++ DLL code is not disclosed. The Input parameters to the strategies and indicators 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 TS manual consists of:

  • A short tutorial on the details of performing walk forward optimization with out-of-sample testing.
  • How I look for the "best" parameters in an optimization run.
  • A complete description of the nCycleGZ system and it's input parameters for E-Mini 5min bars.
  • The walk forward optimization method used and a table of the walk forward results for the 5min bars listing parameter selection, Profit/loss, Drawdown and Largest Losing Trades.
  • The parameter test ranges used.
  • How to setup and use the system and indicators on TradeStation
  • A EasyLanguage code printout.
  • A chart printout of the system and its associated indicator with the out-of-sample period system buy and sell signals displayed on the chart.
  • Performance Summaries for the total time period and the out-of sample segments.

In addition the nCycleGZ system has its exact duplicate in indicator form which is displayable on the price chart and in the charts printout, so that the user can visually see how the buy and sell signals occur.

For NeuroShell Trader/DayTrader Pro

The Trading Strategies and Indicators are directly imported into NeuroShell via a special setup exe file and are fully disclosed in the Manual, Indicator wizard "MA_nCycleGZ" category and in the Trading Strategy Wizard "MA_nCycleGZ" directory. The C++ DLL code is not disclosed. The Input parameters to the strategies and indicators 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 strategy results will give parameters for the intraday or daily futures the strategy was tested on, the user can easily use this system on any tradeable or on any time frame.

The accompanying NS manual consists of:

  • How To Setup A New chart With Data Series, Indicator & Trading Strategy.
  • A complete description of the N cycle Goertzel Indicator & Strategy Input Parameters
  • The N cycle Goertzel Strategy Applied to E-Mini (ES 5 min bars)
  • The Adaptive n Cycle Goertzel DFT Math and Derivation.
  • A Summary Table of All Strategy and Indicator Names

For TradeStation, The Adaptive N cycle Goertzel Discrete Fourier Transform System™ package consisting of manual, DLL files, Strategy(System) and Indicator els or eld files is being offered through Meyers Analytics L.L.C. for $395. Shipping is via Email and consists of the Manual in Adobe PDF format, ELS/ELD file and DLL file. The Adaptive N cycle Goertzel Discrete Fourier Transform System™ DLL file has a "Key Licence" that only allows it to be installed on two computers.

For NeuroShell Trader/DayTrader Pro, The Adaptive N cycle Goertzel Discrete Fourier Transform System™ package consists of a manual as described above and a special setup exe file that installs all the Trading Strategies, Indicators, and DLL into NeuroShell. This product is being offered through Meyers Analytics L.L.C. for $395. Shipping is via Email and consists of a zip file containing the Manual in Adobe PDF format and the MA-nCycleGZSetup.exe setup file. The Adaptive N Cycle Goertzel Discrete Fourier Transform System™ DLL file has a "Key Licence" that only allows it to be installed on two computers.


How To Order
To order online click Order Online. To order via Fax or mail using a Visa or Master Card please fill out the order form on the Order Form page and Fax it to the telephone number on the order form or mail it to the address on the order form. If you would like to talk to me about the product, please call me at (312) 280-1687 M-F 12pm to 5pm CST. All E-mail queries can be sent to support@meyersanalytics.com.

Thank you for your Interest....Dennis Meyers



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