THE INVARIANCE PRINCIPLE FOR LINEAR PROCESSES WITH APPLICATIONS

Qiying Wang (), Yan-Xia Lin and Chandra M. Gulati

Econometric Theory, 2002, vol. 18, issue 1, 119-139

Abstract: Let Xt be a linear process defined by Xt = [sum ]k=0∞ ψkεt−k, where {ψk, k ≥ 0} is a sequence of real numbers and {εk, k = 0,±1,±2,...} is a sequence of random variables. Two basic results, on the invariance principle of the partial sum process of the Xt converging to a standard Wiener process on [0,1], are presented in this paper. In the first result, we assume that the innovations εk are independent and identically distributed random variables but do not restrict [sum ]k=0∞ |ψk|

Date: 2002
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