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.
Author(s): Victor Privalsky
Series: Progress in Geophysics
Publisher: Springer
Year: 2023
Language: English
Pages: 208
City: Cham
Acknowledgements
Contents
Abbreviations
1 Introduction
References
2 Analysis of Scalar Time Series
2.1 Introduction
2.2 Preliminary Processing
2.2.1 No Preliminary Processing Required
2.2.2 Linear Trend
2.2.3 The Hopping Averaging
2.2.4 Seasonal Trend Removal
2.2.5 Linear Filtering
2.3 Time Domain Analysis
2.4 Frequency Domain Analysis
2.5 Statistical Predictability and Prediction
2.6 Verification of GCM-Simulated Climate. The Scalar Case
2.7 Engineering Time Series
2.8 Conclusions
Attachment 2.1: Weights and Frequency Response Functions of Linear Filters
Attachment 2.2: Examples of Optimal Nonlinear Extrapolation of Stationary Random Processes
Introduction
Continuous Markov Random Processes
Disconnected Random Processes
References
3 Bivariate Time Series Analysis
3.1 Introduction
3.2 Products of Bivariate Time Series Analysis with AVESTA3
3.3 Finding Dependence Between Time Series with AVESTA3
3.4 Teleconnection Between Global Temperature and ENSO
3.5 Time Series Reconstruction
3.6 Verification of GCM-Simulated Climate. The Bivariate Case
3.7 Bivariate Analysis of Mechanical Engineering Time Series
3.8 Conclusions
References
4 Analysis of Trivariate Time Series
4.1 Products of Trivariate Time Series Analysis with AVESTA3
4.2 Application to Geophysical Data
4.3 Analysis of Global, Hemispheric, Oceanic, and Terrestrial Data Sets
4.4 Application to Engineering Data
4.5 Conclusions
References
5 Conclusions and Recommendations
References
