×

On residual analysis for time series models. (English) Zbl 0903.62070

Summary: Residuals are frequently used as a diagnostic tool for verification that a time series model fits to data. In the cases when the series is nonnormal and/or the model is nonlinear, the squared residuals and squared values of the series are taken into account. In our paper asymptotic formulas for the mean value and variance of the corresponding sample correlation functions are calculated. Small sample properties are investigated in a simulation study. The results can be used for testing linearity and normality of an autoregressive time series.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62E20 Asymptotic distribution theory in statistics
PDF BibTeX XML Cite
Full Text: EuDML Link

References:

[1] G. E. P. Box, G. M. Jenkins: Models for Prediction and Control. Holden Day, New York 1970.
[2] G. E. P. Box, D. A. Pierce: Distribution of residual autocorrelations in autoregressive-integrated moving average time series models. J. Amer. Statist. Assoc. 65 (1970), 1509-1526. · Zbl 0224.62041
[3] H. Cramer: Mathematical Methods of Statistics. Princeton Univ. Press, Princeton 1946. · Zbl 0063.01014
[4] N. Davies C. M. Triggs, P. Newbold: Significance of the Box-Pierce portmanteau statistics in finite samples. Biometrika 64 (1977), 517-522. · Zbl 0391.62066
[5] A. C. Harvey: Time Series Models. Harvester Wheatsheaf, New York 1993. · Zbl 0878.62061
[6] J. R. M. Hosking, N. Ravishanker: Approximate simultaneous significance intervals for residual autocorrelations of autoregressive moving-average time series models. J. Time Ser. Anal. 14 (1993), 19-26. · Zbl 0825.62689
[7] M. G. Kendall, A. Stuart: The Advanced Theory of Statistics. Vol. I: Distribution Theory. Griffin, London 1969. · Zbl 0223.62001
[8] A. J. Lawrance, P. A. W. Lewis: Higher-order residual analysis for nonlinear time series with autoregressive correlation structure. Internat. Statist. Rev. 55 (1987); 21-35. · Zbl 0612.62122
[9] A. J. Lawrance, P. A. W. Lewis: Reversed residuals in autoregressive time series analysis. J. Time Ser. Anal. 13 (1992), 253-266. · Zbl 0850.62670
[10] G. M. Ljung, G. E. P. Box: On a measure of lack of fit in time series models. Biometrika 65 (1978), 297-303. · Zbl 0386.62079
[11] E. McKenzie: Product autoregression: a time series characterization of the gamma distribution. J. Appl. Probab. 19 (1982), 463-468. · Zbl 0491.60034
[12] A. I. McLeod: On the distribution of residual autocorrelations in Box-Jenkins models. J. Roy. Statist. Soc. Ser. B 40 (1978), 296-302. · Zbl 0407.62065
[13] A. I. McLeod, W. K. Li: Diagnostic checking ARMA time series models using squared-residual autocorrelations. J. Time Ser. Anal. 4 (1983), 269-273. · Zbl 0536.62067
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.