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.
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 accompanying TS manual consists of:
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.
All systems are orientated to short term trading in all bar ranges from 1 tic, to 1 min bars to daily bars. All of the systems have been walk forward tested either on daily data or intraday data.
The accompanying NS manual consists of:
For TradeStation or MultiCharts, The Adaptive N cycle Goertzel Discrete Fourier Transform System package consisting of manual, DLL files, Strategy(System) and Indicator 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, 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 three 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.