Fourier analysis on modeling stock returns of individual companies in bank finance and insurance sector of Sri Lankan share market

Abstract

Sri Lankan share market returns have wave like patterns. A wave can be viewed either in time domain or in the frequency domain. The frequency domain analysis is known as Spectral Analysis or Fourier analysis. Spectral analysis was initially established in physics and engineering. Later it has been applied in explaining the behavior of economic variables exhibiting cyclical or seasonal patterns. However applications of Fourier analysis in economic time series were limited and were unable to find in Sri Lankan context. Current study was focused on applying the Fourier transformation on modeling stock returns of Sri Lankan share market. Random sample of three companies from Bank Finance and Insurance (BFI) sector of Colombo Stock Exchange (CSE) was selected. Monthly average returns from year 2000 to 2011 were used for data analysis. Auto Correlation Functions and Partial Autocorrelation Functions were used to test the stationary of returns. Fourier transformation is used to transform the data into series of trigonometric functions. Multiple Regression analysis was used for estimating amplitudes of the Fourier series and forecasting returns. Normality of residuals and Mean Square Errors (MSE) were used for model validation. Study revealed the ability of applying Fourier transformation on modeling returns of individual companies in BFI sector of CSE. But MSE’s of the models were high. It was recommended to test Fourier transformation on more company returns, representing all the business sectors of CSE. Also it is necessary to find techniques for reducing MSE’s.