Multidimensional Stationary Time Series

This book gives a brief survey of the theory of multidimensional (multivariate), weakly stationary time series, with emphasis on dimension reduction and prediction.

Autorentext

Marianna Bolla, DSc is professor in the Institute of Mathematics, Budapest University of Technology and Economics. She authored the book Spectral Clustering and Biclustering, Learning Large Graphs and Contingency Tables, Wiley (2013) and the article Factor Analysis, Dynamic in Wiley StatsRef: Statistics Reference Online (2017). She is coauthor of a Hungarian book on Multivariate Statistical Analysis and a textbook Theory of Statistical Inference; further, provides lectures on these topics at her home institution and in the Budapest Semesters in Mathematics program. Research interest: spectral clustering, graphical models, time series, application of spectral and block matrix techniques in multivariate regression and prediction, based on classical works of CR Rao.

Tamás Szabados, PhD is a retired associate professor in the Institute of Mathematics, Budapest University of Technology and Economics. He used to give lectures on stochastic analysis and probability theory in his home institute and on probability theory in the Budapest Semesters in Mathematics program as well. He is a coauthor of a Hungarian textbook (1983) on vector analysis. He holds master's degrees in electrical engineering and applied mathematics and PhD in mathematics. Research interests: discrete approximations in stochastic calculus, theory of time series, and mathematical immunology.

Inhalt

1. Harmonic analysis of stationary time series. 2. ARMA, regular, and singular time series in 1D. 3. Linear system theory, state space models. 4. Multidimensional time series. 5. Dimension reduction and prediction in the time and frequency domain. Appendices.