×

Diagnostic checking ARMA time series models using squared-residual autocorrelations. (English) Zbl 0536.62067

Summary: Squared-residual autocorrelations have been found useful in detecting non-linear types of statistical dependence in the residuals of fitted autoregressive-moving average (ARMA) models [cf. C. W. J. Granger and A. P. Andersen, An introduction to bilinear time series models. (1978; Zbl 0379.62074)]. In this note it is shown that the normalized squared-residual autocorrelations are asymptotically unit multivariate normal. The results of a simulation experiment confirming the small- sample validity of the proposed tests is reported.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)

Citations:

Zbl 0379.62074
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] DOI: 10.2307/2034876 · Zbl 0129.10701
[2] DOI: 10.1214/aoms/1177706645 · Zbl 0085.13720
[3] Box G. E. P., Time Series Analysis Forecasting and Control, 2. ed. (1976) · Zbl 0363.62069
[4] Conover W. J., Practical Nonparametric Statistics. (1971)
[5] DOI: 10.2307/2345327
[6] DOI: 10.2307/1909547
[7] Granger C. W., An Introduction to Bilinear Time Series Models (1978) · Zbl 0379.62074
[8] Hannan E. J., Multiple Time Series. (1971) · Zbl 0227.62052
[9] W. K. Li (1981 ) Topics in Time Series Modelling . Ph.D. Thesis . The University of Western Ontario.
[10] DOI: 10.2307/2335207
[11] Marsaglia G., Encyclopedia of Computer Science pp 1192– (1976)
[12] Mcleod A. I., Water Resources Research 14 pp 969– (1978)
[13] A. I. Mcleou, and K. W. Hipel (1978 ) On the Distribution of Residual Autocorrelations in Box-Jenkins Models. J. R. Statist. Soc. B296 -302 . · Zbl 0407.62065
[14] DOI: 10.2307/2286429
[15] Rao C. R., Linear Statistical Inference and Its Applications, 2. ed. (1973) · Zbl 0256.62002
[16] Tong H., J. R. Statist. Soc. B 42 pp 245– (1980)
[17] Whittle P., Bull. Int. Statist. Inst. 33 pp 105– (1961)
[18] Yakowitz S., Water Resources Research 15 pp 1035– (1979)
[19] DOI: 10.1214/aos/1176344687 · Zbl 0407.62060
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.