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Separable lower triangular bilinear model

Part of: Stochastic processes Inference from stochastic processes

Published online by Cambridge University Press:  14 July 2016

Hai-Bin Wang  and
Bo-Cheng Wei
Hai-Bin Wang*
Affiliation:
Southeast University, Nanjing, and Xiamen University
Bo-Cheng Wei*
Affiliation:
Southeast University, Nanjing
*
∗ Postal address: Department of Mathematics, Xiamen University, Xiamen 361005, P. R. China. Email address: dr.whb@163.com
∗∗ Postal address: Southeast University, Nanjing, Si Pai Lou 2#, Nanjing 210096, P. R. China.
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Abstract

The aim of this paper is to analyze the probabilistic structure for a rather general class of bilinear models systematically. First, the 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.

Keywords

Time seriesbilinear modelstationarityautocovariancespectral densitythird-order cumulantsbispectral densityYule–Walker equations

MSC classification

Primary: 62M10: Time series, auto-correlation, regression, etc.
Secondary: 60G10: Stationary processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 1 , March 2004 , pp. 221 - 235
Copyright
Copyright © Applied Probability Trust 2004 

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