Non-causal strictly stationary solutions of random recurrence equations

Dirk-Philip Brandes and Alexander Lindner

Statistics & Probability Letters, 2014, vol. 94, issue C, 113-118

Abstract: Let (Mn,Qn)n∈N be an i.i.d. sequence in R2. Much attention has been paid to causal strictly stationary solutions of the random recurrence equation Xn=MnXn−1+Qn, n∈N, i.e. to strictly stationary solutions of this equation when X0 is assumed to be independent of (Mn,Qn)n∈N. Goldie and Maller (2000) gave a complete characterisation when such causal solutions exist. In the present paper we shall dispose of the independence assumption of X0 and (Mn,Qn)n∈N and derive necessary and sufficient conditions for a strictly stationary, not necessarily causal solution of this equation to exist.

Keywords: Causal; Non-anticipative; Non-causal; Random recurrence equation; Strictly stationary (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1016/j.spl.2014.06.027

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