Multidimensional Stationary Time Series

Dimension Reduction and Prediction

Marianna Bolla author Tamás Szabados author

Format:Hardback

Publisher:Taylor & Francis Ltd

Published:30th Apr '21

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Multidimensional Stationary Time Series cover

This book gives a brief survey of the theory of multidimensional (multivariate), weakly stationary time series, with emphasis on dimension reduction and prediction. Understanding the covered material requires a certain mathematical maturity, a degree of knowledge in probability theory, linear algebra, and also in real, complex and functional analysis. For this, the cited literature and the Appendix contain all necessary material. The main tools of the book include harmonic analysis, some abstract algebra, and state space methods: linear time-invariant filters, factorization of rational spectral densities, and methods that reduce the rank of the spectral density matrix.

  • Serves to find analogies between classical results (Cramer, Wold, Kolmogorov, Wiener, Kálmán, Rozanov) and up-to-date methods for dimension reduction in multidimensional time series
  • Provides a unified treatment for time and frequency domain inferences by using machinery of complex and harmonic analysis, spectral and Smith--McMillan decompositions. Establishes analogies between the time and frequency domain notions and calculations
  • Discusses the Wold's decomposition and the Kolmogorov's classification together, by distinguishing between different types of singularities. Understanding the remote past helps us to characterize the ideal situation where there is a regular part at present. Examples and constructions are also given
  • Establishes a common outline structure for the state space models, prediction, and innovation algorithms with unified notions and principles, which is applicable to real-life high frequency time series

It is an ideal companion for graduate students studying the theory of multivariate time series and researchers working in this field.

" 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.

ISBN: 9780367569327

Dimensions: unknown

Weight: 562g

318 pages