ARMA Model Identification

Overview

During the last two decades, considerable progress has been made in statistical time series analysis. The aim of this book is to present a survey of one of the most active areas in this field: the identification of autoregressive moving-average models, i.e., determining their orders. Readers are assumed to have already taken one course on time series analysis as might be offered in a graduate course, but otherwise this account is self-contained. The main topics covered include: Box-Jenkins' method, inverse ...
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Overview

During the last two decades, considerable progress has been made in statistical time series analysis. The aim of this book is to present a survey of one of the most active areas in this field: the identification of autoregressive moving-average models, i.e., determining their orders. Readers are assumed to have already taken one course on time series analysis as might be offered in a graduate course, but otherwise this account is self-contained. The main topics covered include: Box-Jenkins' method, inverse auorrelation functions, penalty function identification such as AIC, BIC techniques and Hannan and Quinn's method, instrumental regression, and a range of pattern identification methods. Rather than cover all the methods in detail, the emphasis is on exploring the fundamental ideas underlying them. Extensive references are given to the research literature and as a result, all those engaged in research in this subject will find this an invaluable aid to their work.
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Product Details

  • ISBN-13: 9781461397472
  • Publisher: Springer New York
  • Publication date: 3/19/2012
  • Series: Springer Series in Statistics
  • Edition description: Softcover reprint of the original 1st ed. 1992
  • Edition number: 1
  • Pages: 200
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.46 (d)

Table of Contents

1 Introduction.- 1.1 ARMA Model.- 1.2 History.- 1.3 Algorithms.- 1.3.1 AR Parameters.- 1.3.2 MA Parameters.- 1.4 Estimation.- 1.4.1 Extended Yule-Walker Estimates.- 1.4.2 Maximum Likelihood Estimates.- 1.5 Nonstationary Processes.- 1.5.1 Sample ACRF of a Nonstationary Process.- 1.5.2 Iterated Least Squares Estimates.- 1.6 Additional References.- 2 The Auorrelation Methods.- 2.1 Box and Jenkins’ Method.- 2.2 The Inverse Auorrelation Method.- 2.2.1 Inverse Auorrelation Function.- 2.2.2 Estimates of the Spectral Density.- 2.2.3 Estimates of the IACF.- 2.2.4 Identification Using the IACF.- 2.3 Additional References.- 3 Penalty Function Methods.- 3.1 The Final Prediction Error Method.- 3.2 Akaike’s Information Criterion.- 3.2.1 Kullback-Leibler Information Number.- 3.2.2 Akaike’s Information Criterion.- 3.3 Generalizations.- 3.4 Parzen’s Method.- 3.5 The Bayesian Information Criterion.- 3.5.1 Schwarz’ Derivation.- 3.5.2 Kashyap’s Derivation.- 3.5.3 Shortest Data Description.- 3.5.4 Some Comments.- 3.6 Hannan and Quinn’s Criterion.- 3.7 Consistency.- 3.8 Some Relations.- 3.8.1 A Bayesian Interpretation.- 3.8.2 The BIC and Prediction Errors.- 3.8.3 The AIC and Cross-Validations.- 3.9 Additional References.- 4 Innovation Regression Methods.- 4.1 AR and MA Approximations.- 4.2 Hannan and Rissanen’s Method.- 4.2.1 A Three-Stage Procedure.- 4.2.2 Block Toeplitz Matrices.- 4.2.3 A Modification of the Whittle Algorithm.- 4.2.4 Some Modifications.- 4.3 Koreisha and Pukkila’s Method.- 4.4 The KL Spectral Density.- 4.5 Additional References.- 5 Pattern Identification Methods.- 5.1 The 3-Pattern Method.- 5.1.1 The Three Functions.- 5.1.2 Asymptotic Distributions.- 5.1.3 Two Chi-Squared Statistics Ill.- 5.2 The R and S Array Method.- 5.2.1 The R and S Patterns.- 5.2.2 Asymptotic Distributions.- 5.2.3 The RS Array.- 5.3 The Corner Method.- 5.3.1 Correlation Determinants.- 5.3.2 Asymptotic Distribution.- 5.4 The GPAC Methods.- 5.4.1 Woodward and Gray’s GPAC.- 5.4.2 Glasbey’s GPAC.- 5.4.3 Takemura’s GPAC.- 5.5 The ESACF Method.- 5.6 The SCAN Method.- 5.6.1 Eigen-analysis.- 5.6.2 The SCAN Method.- 5.7 Woodside’s Method.- 5.8 Three Systems of Equations.- 5.9 Additional References.- 6 Testing Hypothesis Methods.- 6.1 Three Asymptotic Test Procedures.- 6.2 Some Test Statistics.- 6.3 The Portmanteau Statistic.- 6.4 Sequential Testing Procedures.- 6.5 Additional References.
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