A Blockwise Empirical Likelihood Test for Gaussianity in Stationary Autoregressive Processes

Chioneso S. Marange (), Yongsong Qin, Raymond T. Chiruka and Jesca M. Batidzirai
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Chioneso S. Marange: Department of Statistics, Faculty of Science and Agriculture, Alice Campus, Fort Hare University, Alice 5700, South Africa
Yongsong Qin: College of Mathematics and Statistics, Guangxi Normal University, Guilin 541004, China
Raymond T. Chiruka: Department of Statistics, Faculty of Science and Agriculture, Alice Campus, Fort Hare University, Alice 5700, South Africa
Jesca M. Batidzirai: School of Mathematics, Statistics and Computer Science, Pietermaritzburg Campus, University of KwaZulu-Natal, Pietermaritzburg 3201, South Africa

Mathematics, 2023, vol. 11, issue 4, 1-20

Abstract: A new and simple blockwise empirical likelihood moment-based procedure to test if a stationary autoregressive process is Gaussian has been proposed. The proposed test utilizes the skewness and kurtosis moment constraints to develop the test statistic. The test nonparametrically accommodates the dependence in the time series data whilst exhibiting some useful properties of empirical likelihood, such as the Wilks theorem with the test statistic having a chi-square limiting distribution. A Monte Carlo simulation study shows that our proposed test has good control of type I error. The finite sample performance of the proposed test is evaluated and compared to some selected competitor tests for different sample sizes and a variety of alternative applied distributions by means of a Monte Carlo study. The results reveal that our proposed test is on average superior under the log-normal and chi-square alternatives for small to large sample sizes. Some real data studies further revealed the applicability and robustness of our proposed test in practice.

Keywords: autoregressive; dependent; empirical likelihood; Gaussian; goodness-of-fit; stationary (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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