Fourier analysis for stock price forecasting: Assumption and evidence

Abstract

The research addressed the relevant question whether the Fourier analysis really provides practical value for investors forecasting stock market price. To answer this question, the significant cycles were discovered using the Fourier analysis inside the price series of US stocks; then, the simulation of an agent buying and selling on minima and maxima of these cycles was made. The results were then compared to those of an agent operating chaotically. Moreover, the existing significant cycles were found using more precise methods, suggested in the research, and based on the results of an agent buying and selling on all possible periods and phases. It has been analysed whether these really existing cycles were in accordance with the significant cycles resulting from the Fourier analysis. It has been concluded that the Fourier analysis basically failed. Suchlike failures are expected on similar data series. In addition, momentum and level trading backtests have been used in a similar way. It has been found that the level trading does provide a certain practical value in comparison to the momentum trading method. The research also simplifies the complicated theoretical background for practitioners.

Keyword : algorithmic trading, Fourier’s transformation, FFT, momentum, level trading, US stocks backtesting, market price series spectrogram