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On some distributional properties of a first-order nonnegative bilinear time series model

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Zhiqiang Zhang  and
Howell Tong
Zhiqiang Zhang*
Affiliation:
The University of Hong Kong
Howell Tong*
Affiliation:
The University of Hong Kong
*
∗ Postal address: Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam, Hong Kong.
∗ Postal address: Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam, Hong Kong.
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Abstract

We study a simple first-order nonnegative bilinear time-series model and give conditions under which the model is stationary. The probability density function of the stationary distribution (when it exists) is found. We also discuss the tail behaviour of the stationary distribution and calculate the probability density function by a numerical method. Simulation is used to check the calculation.

Keywords

Bilinear time-series modelessential upper boundessential lower boundsecond-order stationarykey renewal theoremtail behaviour

MSC classification

Primary: 60G17: Sample path properties
Secondary: 60G10: Stationary processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 3 , September 2001 , pp. 659 - 671
Copyright
Copyright © by the Applied Probability Trust 2001 

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