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ESTIMATION FOR THE FIRST‐ORDER DIAGONAL BILINEAR TIME SERIES MODEL
Author(s) -
Kim Won Kyung,
Billard L.,
Basawa I. V.
Publication year - 1990
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1990.tb00053.x
Subject(s) - mathematics , diagonal , estimator , moment (physics) , series (stratigraphy) , bilinear interpolation , least squares function approximation , asymptotic distribution , statistics , white noise , non linear least squares , generalized least squares , paleontology , physics , geometry , classical mechanics , biology
. The problem of estimation of the parameter b in the simple diagonal bilinear model { X t }, X t = e t + be t ‐1 X t ‐1 , is considered, where { e t } is Gaussian white noise with zero mean and possibly unknown variance s̀ 2 . The asymptotic normality of the moment estimator of b is established for the two cases when s̀ 2 is known and s̀ 2 is 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.