Author	Choi, ByoungSeon. author
Title	ARMA Model Identification [electronic resource] / by ByoungSeon Choi
Imprint	New York, NY : Springer US, 1992
Connect to	http://dx.doi.org/10.1007/978-1-4613-9745-8
Descript	XII, 200 p. online resource

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

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 Autocorrelation Methods -- 2.1 Box and Jenkinsโ Method -- 2.2 The Inverse Autocorrelation Method -- 2.3 Additional References -- 3 Penalty Function Methods -- 3.1 The Final Prediction Error Method -- 3.2 Akaikeโs Information Criterion -- 3.3 Generalizations -- 3.4 Parzenโs Method -- 3.5 The Bayesian Information Criterion -- 3.6 Hannan and Quinnโs 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 Rissanenโs Method -- 4.3 Koreisha and Pukkilaโs 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 Woodsideโs 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

1. Mathematics
2. Applied mathematics
3. Engineering mathematics
4. Mathematics
5. Applications of Mathematics