ARMA Model Identification

by ByoungSeon Choi

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 autocorrelation 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.

Product Details

ISBN-13:	9781461397472
Publisher:	Springer New York
Publication date:	03/19/2012
Series:	Springer Series in Statistics
Edition description:	Softcover reprint of the original 1st ed. 1992
Pages:	200
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

1 Introduction.- 1.1 ARMA Model.- 1.2 History.- 1.3 Algorithms.- 1.4 Estimation.- 1.5 Nonstationary Processes.- 1.6 Additional References.- 2 The Auorrelation Methods.- 2.1 Box and Jenkins’ Method.- 2.2 The Inverse Auorrelation Method.- 2.3 Additional References.- 3 Penalty Function Methods.- 3.1 The Final Prediction Error Method.- 3.2 Akaike’s Information Criterion.- 3.3 Generalizations.- 3.4 Parzen’s Method.- 3.5 The Bayesian Information Criterion.- 3.6 Hannan and Quinn’s Criterion.- 3.7 Consistency.- 3.8 Some Relations.- 3.9 Additional References.- 4 Innovation Regression Methods.- 4.1 AR and MA Approximations.- 4.2 Hannan and Rissanen’s Method.- 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.- 5.2 The R and S Array Method.- 5.3 The Corner Method.- 5.4 The GPAC Methods.- 5.5 The ESACF Method.- 5.6 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.