Introduction

Abstract

Most geophysical processes are random, and their analysis should be based upon theory of random processes and information theory. The main tool of analysis here is the autoregressive modeling of scalar and multivariate time series in time and frequency domains. After a brief description of theoretical basis, the scalar case continues from parametric and nonparametric analysis to the final stage—time series prediction. The text includes theory and examples of spectral estimation, description of extrapolation theory, and examples of its application in climatology, oceanography, and meteorology. Multivariate time series analysis is used for describing relations between scalar time series (teleconnections) and for time series reconstructions. The suggested solutions of both tasks disagree with the traditional approach and their advantages are demonstrated, in particular, by investigating a dependence of global surface temperature upon ENSO and reconstructing a simulated time series typical for climate data. A unique climatic process—Quasi-Biennial Oscillation—is analyzed in the frequency domain. Analyses of trivariate time series show the potential of multivariate autoregressive time and frequency domain approach. Time series approach is used for studying ice core, solar, and climate simulation data. The book contains recommendations that help to avoid erroneous steps in time series analysis.