Separable lower triangular bilinear model. (English) Zbl 1045.62091

Wang, Hai-Bin; Wei, Bo-Cheng

J. Appl. Probab. 41, No. 1, 221-235 (2004).

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.

MSC:

62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M15	Inference from stochastic processes and spectral analysis
60G10	Stationary stochastic processes

Keywords:

time series; bilinear model; stationarity; autocovariance; spectral density; third-order cumulants; bispectral density; Yule-Walker equations

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