Using Fourier Transform to Determine Market Cycles

Fourier Transform is one of the most important tools in the modern signal processing world.  It is widely used in communications, geology, acoustic and engineering field.  However, its capability to decompose time series data into frequency domain has extended its usage to other fields such as finance and business (Read more here).

In finance, moving average is a common indicator to track the movement of the stock market.  However, the period of the moving average indicator is normally selected at the discretion of the users, which sometimes may not be appropriate.  Fourier Transform is a good tool to determine the period for the moving average.  The following graph shows the significant period of the KLCI daily closing price determined by Fourier Transform.

From the graph, short term significant periods are 8 and 17 days while medium term significant periods are 28, 43, and 61 days.  Fourier Transform computations could be found in popular engineering software such as MATLAB or common financial tool such as Excel Analysis ToolPak (Read more here).