Multidimensional Stationary Time Series: Dimension Reduction and Prediction
暫譯: 多維靜態時間序列：降維與預測
Bolla, Marianna, Szabados, Tamás
- 出版商: CRC
- 出版日期: 2021-04-30
- 售價: $6,190
- 貴賓價: 9.5 折 $5,881
- 語言: 英文
- 頁數: 292
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 0367569329
- ISBN-13: 9780367569327
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商品描述
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, K lm n, 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.
商品描述(中文翻譯)
這本書簡要概述了多維（多變量）弱平穩時間序列的理論，重點在於降維和預測。理解所涵蓋的內容需要一定的數學成熟度，以及在概率論、線性代數、實分析、複分析和泛函分析方面的知識。為此，引用的文獻和附錄包含了所有必要的材料。本書的主要工具包括調和分析、一些抽象代數以及狀態空間方法：線性時間不變濾波器、有理譜密度的因式分解，以及降低譜密度矩陣秩的方法。
* 用於尋找經典結果（Cramer、Wold、Kolmogorov、Wiener、K lm n、Rozanov）與當前多維時間序列降維方法之間的類比。
* 通過使用複分析和調和分析的工具、譜分解和Smith--McMillan分解，提供時間和頻率域推斷的統一處理。建立時間和頻率域概念及計算之間的類比。
* 討論Wold分解和Kolmogorov分類，並區分不同類型的奇異性。理解遙遠的過去有助於我們描述當前存在的理想情況，即有一個規則的部分。還提供了示例和構造。
* 為狀態空間模型、預測和創新算法建立了一個共同的框架結構，具有統一的概念和原則，適用於現實生活中的高頻時間序列。
這是研究多變量時間序列理論的研究生和在該領域工作的研究人員的理想伴侶。
作者簡介
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.
作者簡介(中文翻譯)
Marianna Bolla，DSc，是布達佩斯科技經濟大學數學研究所的教授。她著有《Spectral Clustering and Biclustering, Learning Large Graphs and Contingency Tables》，Wiley（2013）以及文章《Factor Analysis, Dynamic》收錄於Wiley StatsRef: Statistics Reference Online（2017）。她是一本關於多變量統計分析的匈牙利書籍的共同作者，並且是教科書《Theory of Statistical Inference》的共同作者；此外，她在本校及布達佩斯數學學期計畫中提供這些主題的講座。研究興趣：光譜聚類、圖形模型、時間序列、在多變量回歸和預測中應用光譜和區塊矩陣技術，基於CR Rao的經典著作。
Tamás Szabados，PhD，是布達佩斯科技經濟大學數學研究所的退休副教授。他曾在本校教授隨機分析和概率論，並在布達佩斯數學學期計畫中教授概率論。他是一本關於向量分析的匈牙利教科書（1983）的共同作者。他擁有電機工程和應用數學的碩士學位，以及數學的博士學位。研究興趣：隨機微積分中的離散近似、時間序列理論和數學免疫學。
