Multidimensional Stationary Time Series: Dimension Reduction and Prediction

This book provides a comprehensive survey of the theory of multidimensional (multivariate), weakly stationary time series, with an emphasis on dimension reduction and prediction. It requires a certain mathematical maturity and knowledge in probability theory, linear algebra, and real, complex, and functional analysis. The main tools of the book include harmonic analysis, abstract algebra, and state space methods. It establishes analogies between classical results and up-to-date methods for dimension reduction, and discusses the Wold's decomposition and the Kolmogorov's classification. It is an ideal companion for graduate students studying the theory of multivariate time series and researchers working in this field.

\n Format: Hardback
\n Length: 270 pages
\n Publication date: 28 April 2021
\n Publisher: Taylor & Francis Ltd
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This comprehensive book offers a thorough exploration of the theory of multidimensional (multivariate) weakly stationary time series, placing particular emphasis on dimension reduction and prediction. To fully grasp the material covered, a certain level of mathematical maturity, proficiency in probability theory, linear algebra, and real, complex, and functional analysis is essential. The cited literature and the Appendix provide all the necessary materials for further study.

The book employs a range of powerful tools, including harmonic analysis, abstract algebra, and state space methods. These tools include linear time-invariant filters, factorization of rational spectral densities, and methods for reducing the rank of the spectral density matrix. By employing these techniques, the book facilitates the discovery of analogies between classical results obtained by renowned scholars such as Cramer, Wold, Kolmogorov, Wiener, Kálmán, Rozanov, and others, and up-to-date methods for dimension reduction in multidimensional time series.

The book provides a unified treatment for time and frequency domain inferences by utilizing complex and harmonic analysis, spectral and Smith--McMillan decompositions. This approach enables the establishment of connections between time and frequency domain notions and calculations, offering a comprehensive framework for understanding multidimensional time series. Furthermore, the book delves into the Wold's decomposition and the Kolmogorov's classification, distinguishing between different types of singularities. Understanding the remote past helps in characterizing the ideal situation where a regular part exists at present. Examples and constructions are provided to illustrate the theoretical concepts.

Establishing a common outline structure for state space models, prediction, and innovation algorithms with unified notions and principles is a key feature of the book. This structure is applicable to real-life high-frequency time series and serves as an ideal companion for graduate students studying the theory of multivariate time series and researchers working in this field.

In conclusion, this book is a valuable resource for anyone seeking to gain a deeper understanding of multidimensional weakly stationary time series. Its comprehensive coverage, rigorous analysis, and practical applications make it an essential tool for scholars, researchers, and practitioners in the field.

\n Weight: 576g\n
Dimension: 229 x 244 x 23 (mm)\n
ISBN-13: 9780367569327\n \n