Nonlinear Time Series: Theory, Methods and Applications with R Examples (Chapman & Hall/CRC Texts in Statistical Science)

Randal Douc, Eric Moulines, David Stoffer

  • 出版商: Chapman and Hall/CRC
  • 出版日期: 2014-01-06
  • 售價: $5,540
  • 貴賓價: 9.5$5,263
  • 語言: 英文
  • 頁數: 551
  • 裝訂: Hardcover
  • ISBN: 1466502258
  • ISBN-13: 9781466502253
  • 相關分類: R 語言
  • 海外代購書籍(需單獨結帳)

買這商品的人也買了...

商品描述

Designed for researchers and students, Nonlinear Times Series: Theory, Methods and Applications with R Examples familiarizes readers with the principles behind nonlinear time series models―without overwhelming them with difficult mathematical developments. By focusing on basic principles and theory, the authors give readers the background required to craft their own stochastic models, numerical methods, and software. They will also be able to assess the advantages and disadvantages of different approaches, and thus be able to choose the right methods for their purposes.

 

The first part can be seen as a crash course on "classical" time series, with a special emphasis on linear state space models and detailed coverage of random coefficient autoregressions, both ARCH and GARCH models. The second part introduces Markov chains, discussing stability, the existence of a stationary distribution, ergodicity, limit theorems, and statistical inference. The book concludes with a self-contained account on nonlinear state space and sequential Monte Carlo methods. An elementary introduction to nonlinear state space modeling and sequential Monte Carlo, this section touches on current topics, from the theory of statistical inference to advanced computational methods.

 

The book can be used as a support to an advanced course on these methods, or an introduction to this field before studying more specialized texts. Several chapters highlight recent developments such as explicit rate of convergence of Markov chains and sequential Monte Carlo techniques. And while the chapters are organized in a logical progression, the three parts can be studied independently.

 

Statistics is not a spectator sport, so the book contains more than 200 exercises to challenge readers. These problems strengthen intellectual muscles strained by the introduction of new theory and go on to extend the theory in significant ways. The book helps readers hone their skills in nonlinear time series analysis and their applications.

商品描述(中文翻譯)

《非線性時間序列:理論、方法和R實例應用》是為研究人員和學生設計的,旨在使讀者熟悉非線性時間序列模型的原則,而不會讓他們被困難的數學發展所淹沒。通過專注於基本原理和理論,作者為讀者提供了製作自己的隨機模型、數值方法和軟件所需的背景知識。他們還能夠評估不同方法的優缺點,從而能夠為自己的目的選擇合適的方法。

第一部分可以看作是關於“傳統”時間序列的速成課程,特別強調線性狀態空間模型和對隨機係數自回歸(包括ARCH和GARCH模型)的詳細介紹。第二部分介紹了馬爾可夫鏈,討論了穩定性、存在平穩分佈、遞歸性、極限定理和統計推斷。本書以非線性狀態空間和序列蒙特卡羅方法作為結尾。這一部分對非線性狀態空間建模和序列蒙特卡羅進行了初步介紹,觸及了從統計推斷理論到高級計算方法的當前主題。

本書可作為進階課程的輔助教材,或在學習更專門的文獻之前對這一領域進行介紹。幾個章節突出了最近的發展,如馬爾可夫鏈的收斂速率和序列蒙特卡羅技術。雖然章節按照邏輯順序組織,但三個部分可以獨立學習。

統計學不是一項旁觀者運動,因此本書包含200多個練習題,以挑戰讀者。這些問題可以加強對新理論的理解,並以重要的方式擴展理論。本書幫助讀者提高他們在非線性時間序列分析及其應用方面的技能。