کتاب دانلود کتب لاتین علوم مهندسیسایر موارد
سری زمانی ثابت چند بعدی - کاهش و پیش بینی بعد
سری زمانی ثابت چند بعدی - کاهش و پیش بینی بعد

Multidimensional Stationary Time Series - Dimension Reduction and Prediction
سال انتشار: 2021
تعداد صفحات: 296
زبان فایل: انگلیسی
فرمت فایل: pdf
حجم فایل: 10MB
قیمت: 200,000ريال

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Publisher : Chapman and Hall/CRC

ISBN-10 : 0367569329

ISBN-13 : 978-0367569327

ASIN : B091GNX352

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.