Frequency Domain Analysis

Abstract

The results discussed in chapter 3 reveal the existence of trends in the data. The results from trend tests, however, suggest that this variability is more likely to be non-monotonic in nature; i.e. periodic or cyclic. Spectral analysis in the frequency domain is suitable for analyzing cyclic behavior in time series. The basic idea of spectral analysis is to represent the time series as a sum of sinusoidal components of different frequencies. The power spectrum of a time series, which is the squared amplitude of these sinusoids reflects the distribution of the variance of the stochastic process over these frequencies. By studying the power spectrum, those cyclic components which contribute most to the overall variability of the time series can be identified. The shape of the spectrum also reveals features of the process that are useful in selecting the types of models which are suitable for analyzing the observed data (Jenkins and Watts, 1968).