Athreya, Krishna B. ; Saha, Koushik ; Srivastava, Radhendushka
(2017)
*AR(1) sequence with random coefficients: Regenerative properties and its application*
Probability
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Official URL: https://arxiv.org/abs/1709.03753

## Abstract

Let {Xn}n≥0 be a sequence of real valued random variables such that Xn=ρnXn−1+ϵn, n=1,2,…, where {(ρn,ϵn)}n≥1 are i.i.d. and independent of initial value (possibly random) X0. In this paper it is shown that, under some natural conditions on the distribution of (ρ1,ϵ1), the sequence {Xn}n≥0 is regenerative in the sense that it could be broken up into i.i.d. components. Further, when ρ1 and ϵ1 are independent, we construct a non-parametric strongly consistent estimator of the characteristic functions of ρ1 and ϵ1.

Item Type: | Article |
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Source: | Copyright of this article belongs to arXiv |

Keywords: | Probability (math.PR), FOS: Mathematics, FOS: Mathematics, 60G20 |

ID Code: | 131547 |

Deposited On: | 07 Dec 2022 05:27 |

Last Modified: | 07 Dec 2022 05:27 |

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