AR(1) Sequence with Random Coefficients:Regenerative Properties and its Application

Krishna B Athreya, Koushik Saha, Radhendushka Srivastava
2017 Communications on Stochastic Analysis  
Let {Xn} n≥0 be a sequence of real valued random variables such that Xn = ρnX n−1 + ϵn, n = 1, 2, . . ., where {(ρn, ϵn)} n≥1 are i.i.d. and independent of initial value (possibly random) X 0 . In this paper it is shown that, under some natural conditions on the distribution of (ρ 1 , ϵ 1 ), the sequence {Xn} n≥0 is regenerative in the sense that it could be broken up into i.i.d. components. Further, when ρ 1 and ϵ 1 are independent, we construct a non-parametric strongly consistent estimator of the characteristic functions of ρ 1 and ϵ 1 .
doi:10.31390/cosa.11.3.07 fatcat:w6vo4u2ctfc2faaz47g2wp7t5e