Adaptative Locally Asymptotically Optimal Test for Random Effects in GARMA Model

Oumaima  Essefiani; Said  Hamdoune; Rachid  El Halimi; Aziz  Lmakri

Authors

Oumaima Essefiani Mathematics and Applications Laboratory, Faculty of Sciences and Techniques, Abdelmalek Essaadi University, Tangier, Morocco
Said Hamdoune Mathematics and Applications Laboratory, Faculty of Sciences and Techniques, Abdelmalek Essaadi University, Tangier, Morocco
Rachid El Halimi Mathematics and Applications Laboratory, Faculty of Sciences and Techniques, Abdelmalek Essaadi University, Tangier, Morocco
Aziz Lmakri AIMCE Laboratory, ENSAM, Hassan II University, Casablanca, Morocco

Keywords:

Long memory time series, GARMA model, local asymptotic normality, pseudo-Gaussian test, rank test

Abstract

The main purpose of this paper is to develop a locally asymptotically optimal statistical new test for detecting the presence of random parameters in a Generalized Autoregessive Moving Average (GARMA) process. The purpose of the procedure study is to derive the powerful test for the hypothesis that the GARMA coefficients are constant overtime against the alternative that vary according to random effects. The asymptotic distribution and its tests properties are established under the local asymptotic normality. It is shown that the proposed test statistic is; consistent, locally asymptotically optimal, performs better than the competing tests available in the literature, and constitutes a powerful technical tool for detecting the random effects in GARMA models. A simulation study was carried out to investigate the performance of this procedure. In fact, Monte Carlo method shows that the test has very good power for all cases considered. Additionally, a real data analysis is conducted to examine the performance of this procedure.

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