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STATIONARITY AND CENTRAL LIMIT THEOREM ASSOCIATED WITH BILINEAR TIME SERIES MODELS
Author(s) -
Chanda Kamal C.
Publication year - 1991
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.1467-9892.1991.tb00085.x
Subject(s) - mathematics , ergodic theory , central limit theorem , combinatorics , series (stratigraphy) , limit (mathematics) , bilinear interpolation , asymptotic distribution , pure mathematics , mathematical analysis , estimator , statistics , paleontology , biology
. Consider the general bilinear times series modelwhere { X t ; t = 0, L1, …} is a p ‐variate process, C ( p x ( s + 1)), A ( p x p ). B t ( p x p ) (1 ≤ j ≤ q ) are arbitrary matrices of constants, εT=[εt,…εt‐q+1] and {εt; t=0, ±1, …} is a strictly stationary ergodic sequence of random variables. We investigate a set of minimal regularity conditions (on C, A, B j and {ε t }) under which we can establish the existence and causality of X t and the asymptotic normality of the sample mean derived from { X t }.