Practical Time Series Analysis in Natural Sciences: Progress in Geophysics

This book presents an easy-to-use tool for time series analysis and allows the user to concentrate upon studying time series properties rather than upon how to calculate the necessary estimates. The two attached programs provide, in one run of the program, a time and frequency domain description of scalar or multivariate time series approximated with a sequence of autoregressive models of increasing orders. The optimal orders are chosen by five order selection criteria. The results for scalar time series include time domain stochastic difference equations, spectral density estimates, predictability properties, and a forecast of scalar time series based upon the Kolmogorov-Wiener theory. For the bivariate and trivariate time series, the results contain a time domain description with multivariate stochastic difference equations, statistical predictability criterion, and information for calculating feedback and Granger causality properties in the bivariate case. The frequency domain information includes spectral densities, ordinary, multiple, and partial coherence functions, ordinary and multiple coherent spectra, gain, phase, and time lag factors. The programs seem to be unique and using them does not require professional knowledge of theory of random processes. The book contains many examples including three from engineering.