Asymptotic distribution of the bootstrap parameter estimator for AR(1) process

Article type: Research Article

Authors: Suprihatin, Bambang^{a; *} | Guritno, Suryo^b | Haryatmi, Sri^b

Affiliations: [a] Mathematics Department at University of Sriwijaya, Palembang, Indonesia | [b] Mathematics Department at University of Gadjah Mada, Yogyakarta, Indonesia

Correspondence: [*] Corresponding author: Bambang Suprihatin, Mathematics Department at University of Sriwijaya, Palembang, Indonesia. E-mail: [email protected].

Abstract: In this paper we investigated the asymptotic distribution of the bootstrap parameter estimator of a first order autoregressive AR(1) model. We described the asymptotic distribution of such estimator by applying the delta method and employing two different approaches, and concluded that the two approaches lead to the same conclusion, viz. both results converge in distribution to a normal distribution. We also presented the Monte Carlo simulation of the residuals bootstrap and application with real data was carried out in order to yield apparent conclusions.

Keywords: Asymptotic distribution, autoregressive, bootstrap, delta method, Monte Carlo simulation

DOI: 10.3233/MAS-140311

Journal: Model Assisted Statistics and Applications, vol. 10, no. 1, pp. 53-61, 2015