Table of Contents

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.

About the Author

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.

Reviews

" The book is a well-structured point of view of time series theory, contains many theorems along with proofs. In addition, the book presents the necessary lemmas, definitions, and remarks. It should be noted, that at the end of the book in the form of appendices you can find the material needed to understand the theory of time series – tools from linear algebra, matrix theory and complex analysis. So, the book "Multidimensional Stationary Time Series: Dimension Reduction and Prediction" by Marianna Bolla and Tamas Szabados is a very good guide for specialists in time series predictions and dimension reduction."Taras Lukashiv, Ukraine, ISCB News, June 2022."Marianna Bolla and Tamás Szabados provide a comprehensive book discussing the theory of
multidimensional (multivariate), weakly stationary time series, emphasizing dimension
reduction and prediction. The authors delve heavily into the analytical details that would require
advanced knowledge in probability theory and linear algebra along with real and complex analysis.
That said, the cited literature and the book’s appendix contain all the necessary material to
assist readers with the mathematical details used in the analytical derivations."Brian W. Sloboda, University of Maryland, U.S.A, International Statistical Review, 2024.