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On the autocorrelation structure and identification of some bilinear time series. (English) Zbl 0546.62062

Summary: For the bilinear time series \(X_ t=\beta X_{t-k}e_{t-l}+e_ l\), \(k\geq l\), formulas for the first k-1 autocorrelations of \(X^ 2_ t\) are obtained. These results fill in a gap in C. W. J. Granger and A. P. Andersen, An introduction to bilinear time series models. (1978; Zbl 0379.62074). Simulation experiments are used to study the applicability of theoretical results and to investigate some more general situations. It is found that if \(\beta\) is not too small, k and l may be identified using the autocorrelations of \(X^ 2_ t\). Application to more general situations is also briefly discussed.

MSC:

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

Citations:

Zbl 0379.62074
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References:

[1] Box G. E. P., Time Series, Forecasting and Control (1976) · Zbl 0363.62069
[2] Gabr M., J. Time Series Anal. 2 pp 155– (1981)
[3] Granger C. W. J., Introduction to Bilinear Time Series Models (1978) · Zbl 0379.62074
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[5] DOI: 10.1016/0304-4149(82)90044-8 · Zbl 0481.62073 · doi:10.1016/0304-4149(82)90044-8
[6] DOI: 10.2307/1391774 · doi:10.2307/1391774
[7] DOI: 10.1016/0304-4149(82)90045-X · Zbl 0485.62100 · doi:10.1016/0304-4149(82)90045-X
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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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.