Adaptive Estimation of Periodic First-Order Threshold Autoregressive Model

Abstract

Asymptotic properties satisfied by its central sequence. Using these results, we construct adaptive estimators for the parameter model where the innovation density is unspecified but symmetric, while satisfying only some general conditions. The performances of these adaptive estimations are shown via simulation studies and an application on the modeling of the Fraser River data.

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.…”