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Books > Science & Mathematics > Mathematics > Probability & statistics
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Multidimensional Stationary Time Series - Dimension Reduction and Prediction (Hardcover)
Loot Price: R4,153
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Multidimensional Stationary Time Series - Dimension Reduction and Prediction (Hardcover)
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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, Kalman,
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.
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