Adaptive Estimation of Causal Periodic Autoregressive Model

Abstract

This article deals with the adaptive estimation of a periodic autoregressive model, with unspecified innovation density satisfying only some general technical assumptions. We first establish, while verifying the adapted sufficient conditions of Swensen (1985) to our model, the Local Asymptotic Normality (LAN), the Local Asymptotic Quadratic (LAQ), and the Local Asymptotic properties satisfied by its central sequence. Secondly, the Locally Asymptotically Minimax (LAM) estimators are constructed. Using these results, we construct the adaptive estimators of the unknown autoregressive parameters. The performances of the established estimators are shown, via simulation studies.

Locally asymptotically efficient estimation for parametric PINAR(p) models

“…Since this pioneering paper, several works in the context of efficient estimation based on the (LAN) property have seen the day. Among these works, we can quote without claiming exhaustivity some examples: Koul and Schick (1996), for the estimation of the parameters of an AR process with random coefficients, Bentarzi, Guerbyenne, and Merzougui (2009), for the parameters estimation problem of the AR model with periodic coefficients, and Bentarzi and Djeddou (2014), for the estimating in periodically correlated SETAR process. We emphasize that these last works cited, treat only the case where the distribution of innovation belongs to a family of symmetrical distributions.…”