Two chi-square statistics for determining the orders p and q of an ARMA (p, q) process

Author

Choi, ByoungSeon

Author_Institution

Dept. of Appl. Stat., Yonsei Univ., Seoul, South Korea

Volume

41

Issue

6

fYear

1993

fDate

6/1/1993 12:00:00 AM

Firstpage

2165

Lastpage

2176

Abstract

The θ, λ, and η functions have been previously proposed for use in choosing the autoregressive and moving-average orders of an ARMA (q, p) process visually. Two chi-square statistics associated with these three functions are presented and used here to determine the orders of an ARMA process statistically. It is shown that the two statistics are asymptotically equivalent to the Quenouille-Walker´s goodness-of-fit test statistic, which is a Lagrange multiplier test statistic. Some numerical examples are presented to illustrate the usefulness of the two chi-square statistics as well as the three functions in ARMA modeling

Keywords

parameter estimation; signal processing; statistical analysis; η functions; λ functions; &thetas; functions; ARMA (p, q) process; Lagrange multiplier test statistic; Quenouille-Walker´s goodness-of-fit test statistic; autoregressive order; chi-square statistics; moving average order; numerical examples; signal processing; Autocorrelation; Difference equations; Lagrangian functions; Parameter estimation; Statistical analysis; Statistics; Stochastic processes; Testing; Yttrium;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.218144

Filename

218144