On the general bilinear time series model
- 1 September 1988
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 25 (3) , 553-564
- https://doi.org/10.2307/3213984
Abstract
A sufficient condition is derived for the existence of a strictly stationary solution of the general bilinear time series equations. The condition is shown to reduce to the conditions of Pham and Tran (1981) and Bhaskara Rao et al. (1983) in the special cases which they consider. Under the condition specified, a solution is constructed which is shown to be causal, stationary and ergodic. It is moreover the unique causal solution and the unique stationary solution of the defining equations. In the special case when the defining equations contain no non-linear terms, our condition reduces to the well-known necessary and sufficient condition for existence of a causal stationary solution.Keywords
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