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Working Papers

 The Adaptive N Cycle Goertzel Discrete Fourier Transform System

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 Strategy.
See working paper entitled "Trading DIA ETF 5min bars Using the Goertzel Cycle v2 Strategy with Walk-Forward 20 trading days in-sample and 1 trading day out-of-sample 12/9/2019 to 7/9/2021" 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 and phases with the highest amplitudes. Using those N frequencies, amplitudes and phases, we will construct a new price that forecasts the price 1 bar ahead. We will save this 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.

For TradeStation or Multicharts
All of the EasyLanguage strategy and indicator codes are directly importable into TS9,10 and MultiCharts 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 their own input parameter set on their price series and time frame of interest.

In addition the nCycleGZ strategy 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.

All GZ strategies are orientated to short term trading in all bar ranges from 1 tic, to 1 min bars to daily bars.

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

How To Order
To order online click Order Online. If you would like to talk to me about the product, please call me at (312) 767-7640 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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