A SIMPLE CONDITION FOR THE EXISTENCE OF SOME STATIONARY BILINEAR TIME SERIES

Jian Liu

Journal of Time Series Analysis, 1989, vol. 10, issue 1, 33-39

Abstract: Abstract. A sufficient condition is derived for the existence of a strictly stationary solution of some bilinear time series which may have infinite variance innovations. This condition is equivalent to the condition that a polynomial of degree r has no zeros within the unit circle. In the special case when the innovations have finite variance, the computational effort involved in checking this condition is significantly reduced compared with checking the stationarity conditions given by Bhaskara Rao et al. and Liu and Brockwell which requires a knowledge of the maximum eigenvalue in the absolute value of an r2 x r2 matrix.

Date: 1989
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