| Abstract: | ![]()
The basic concepts and application of spectral analysis are explained. Stationary time series and autocorrelation are first defined. Autocorrelation is related to the familiar concepts of variance and covariance. The use of autocorrelation analysis is explained in estimating the interdependent relationship of a time series over discrete time lags. In order to measure the behavior of the time series using autocorrelation, it would be necessary to examine a very large number of autocorrelation lags. Alternatively, the technique of Fourier analysis can be used to transform the autocorrelation function of the time series into a continuous function, termed a spectrum. The spectrum has a one to one correspondence to the autocorrelation for the time series and has the advantage of representing all possible autocorrelations over the discrete time lags. The spectrum can then be examined as a measure of the behavior of the time series. Spectral analysis indicates the reliability of the analysis of autocorrelated variables when familiar statistical techniques such as sample means and variances are used. The application of spectral analysis to management science problems in three general areas is illustrated: (1) inventory demand, (2) transportation simulation, and (3) stock market price behavior. Spectral analysis was used to detect cycles and trends in the data. Analyses were focused on the spectrum which provides a measure of the relative contribution of cycles in a band of frequencies to the total variance of the data. |
