On the Performance and Estimation of Spectral and Bispectral Analysis of Time Series Data

In this study, discrete spectral and bi-spectral analysis of time series data were considered to determine which of them perform better. The parameters of the spectral and bi-spectral models were estimated using Modified Newton Raphson Iterative method. Since the order of a model cannot be increased indiscriminately because of the closeness of some parameters to zero; discrete spectral and bi-spectral analysis model of orders one to five were fitted to the real series. Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) were used to determine the best order of the model. To determine the best model, the residual variance attached to the spectral and bi-spectral models was used. Order one and order four gave the best order in spectral and bi-spectral models, respectively. Residual variances of spectral and bi-spectral models compared favourably with each other. The residual variance of bi-spectral model was smaller than the residual variance of spectral model and this made us to conclude that bi-spectral analysis of time series data performed better than spectral analysis of time series data.