| Abstract: | ![]()
Although spectral analysis has previously been discussed in a number of business journals, the discussion has not been detailed enough for non-mathematicians. The objective of this paper is to review in detail the concepts and to go over the computations of spectral analysis as they pertain to forecasting. To gain insight into the model building technique of spectral analysis, a passing comparison with a familiar model–regression–is made. Regression analysis attempts to find a set of independent variables that shed some light on the dependent variable to be forecasted. In other words, if the independent variables have some functional relationship with the dependent variable, a reliable forecast of the dependent variable can then be made. Forecasting using spectral analysis, on the other hand, is based on the assumption that the variation of a time series can be explained by some mixture of sine and cosine waves. Model parameters can then be estimated for these waves and forecasts be made. These parameters have the same property of least squares as in ordinary regression analysis. A transformation of these parameters gives the spectra of the time series. The spectra are related to the explained variation present in regression analysis. An extension of the spectra gives a set of coefficients of an autoregressive forecasting model. This latter model is referred to as the Wiener-Kolmogorov forecasting model. |
