DISTINCTION BETWEEN SPEPECTRAL ANALYSIS AND HARMONIC ANALYSIS IN TIME SERIES ANALYSIS: EXPERIENCE FROM THE NUMBER CRUNCHER STATISTICAL SYSTEM (NCSS) SOFTWARE.

Abstract

This paper shows a clear distinction between Spectral Analysis and Harmonic Analysis and highlights what is common amongst these two terms. The distinction and commonalities are illustrated using the data from sales of cement obtained from a sales record. The work identified the role of spectral analysis as that of showing the periods /wavelengths having containing more energy with the sine and cosine components but without stating whether the components are significant or not. Spectral analysis helps to identify hidden periodicities but does not form the model equation. Harmonic analysis on the other hand makes use of the periods with higher energies identified by the spectral analysis to form a model equation, it also shows whether the frequencies are significant or not by displaying the t-values for each  k^th harmonic value used to form the model equation. From the giving data, harmonic analysis makes predictions /forecasts, performs model parameter estimation, Analysis of variance, displays the asymptotic correlation matrix of parameters. In harmonic analysis, the graphs of errors against time and against the predicted values are also plotted.