ESTIMATION FOR THE FIRST‐ORDER DIAGONAL BILINEAR TIME SERIES MODEL
- 1 May 1990
- journal article
- Published by Wiley in Journal of Time Series Analysis
- Vol. 11 (3) , 215-229
- https://doi.org/10.1111/j.1467-9892.1990.tb00053.x
Abstract
The problem of estimation of the parameterbin the simple diagonal bilinear model {Xt},Xt=et+bet‐1Xt‐1, is considered, where {et} is Gaussian white noise with zero mean and possibly unknown variance s̀2. The asymptotic normality of the moment estimator ofbis established for the two cases when s̀2is known and s̀2is unknown. It is noted that the limit distribution of the least‐squares cannot easily be derived analytically. A bootstrap comparison of the sampling distributions of the least‐squares and moment estimates shows that both are asymptotically normal with the least‐squares estimate being the more efficient.Keywords
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