Bispectral density computation and its application to time series analysis

Abstract

Prediction and simulation are the main purposes of the time series data analysis. In order to obtain good results, one needs to fitting of an appropriate model for the given time series data. Early time series model fittings were concerned with the fitting of linear type models, namely, ARMA models. But in many cases, time series come from some non-linear process. Consequently, linear models fail to produce satisfactory results. In recent years, neural network approaches are used satisfactorily to deal with almost all type of time series. Spectral density also plays an important role in time series analysis. Particularly, when the data emerges from a linear and Gaussian process, it contains all the necessary and useful information about the series. However, in order to deal with non-linear and non-Gaussian processes, we need to consider higher order spectra. The simplest higher order spectra is bispectra. In this thesis, we have computed bispectral density and have used it in testing the linearity and Gaussianity properties of the time series for ECG and WIND data. Based on the outcome of this test appropriate models are fitted for the data sets considered. The fitted model is then used for one point prediction and simulation of the original series. It is found that Multistep prediction collapses within a few steps. This is not the case in neural network approach.