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Separable lower triangular bilinear model. (English) Zbl 1045.62091
Summary: The aim of this paper is to analyze the probabilistic structure for a rather general class of bilinear models systematically. First, sufficient and necessary conditions for stationarity are given with a concise expression. Then both the autocovariance function and the spectral density function are obtained. The Yule-Walker-type difference equations for autocovariances are derived by means of the spectral density function. Concerning the second-order probabilistic structure, the model is similar to an ARMA model. The third-order probabilistic structure for the model is discussed and a group of Yule-Walker-type difference equations for third-order cumulants are discovered.

62M10Time series, auto-correlation, regression, etc. (statistics)
62M15Spectral analysis of processes
60G10Stationary processes
Full Text: DOI
[1] Granger, C. W. J. and Anderson, A. P. (1978). An Introduction to Bilinear Time Series Models . Vandenhoeck and Ruprecht, Gottingen. · Zbl 0379.62074
[2] Liu, J. and Brockwell, P. J. (1988). On the general bilinear time series model. J. Appl. Prob. 25 , 553--564. · Zbl 0654.60029 · doi:10.2307/3213984
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[8] Subba Rao, T. (1983). The bispectral analysis of nonlinear stationary time series with reference to bilinear time series models. In Handbook of Statistics , Vol. 3, Time Series in the Frequency Domain , eds D. R. Brillinger and P. R. Krishnaiah, North-Holland, Amsterdam, pp. 293--319. · Zbl 0537.62076
[9] Subba Rao, T. and Gabr, M. (1984). An Introduction to Bispectral Analysis and Bilinear Time Series Models (Lecture Notes Statist. 24 ). Springer, New York. · Zbl 0543.62074
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