Preliminary Test Estimation for Parallel 2-Sampling in Autoregressive Model

Syed Ejaz Ahmed, Arsalane Chouaib Guidoum () and Sara Bendjeddou
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Syed Ejaz Ahmed: Department of Mathematics and Statistics, Brock University, 1812 Sir Isaac Brock Way, St. Catharines, ON L2S 3A1, Canada
Arsalane Chouaib Guidoum: Department of Mathematics and Computer Science, Faculty of Sciences and Technology, University of Tamanghasset, Tamanghasset 11000, Algeria
Sara Bendjeddou: Laboratory MSTD, Faculty of Mathematics, University of Science and Technology Houari Boumediene, P.O. Box 32, El Alia 16111, Algeria

Stats, 2024, vol. 7, issue 4, 1-18

Abstract: The purpose of this paper is to discuss the problem of estimation and testing the equality of two autoregressive parameters of two first-order autoregressive processes AR ( 1 ) , where for each process, the observations are made at different time points. The primary interest is to propose the testing procedures for the homogeneity of autocorrelation parameters ρ 1 and ρ 2 . Furthermore, we are interested in estimating ρ 1 under uncertain and weak prior information about the possible equality of ρ 1 and ρ 2 , though we may not have full confidence in the tenacity of this information. A large sample test for the homogeneity of the parameters is developed. Pooled “P” (or restricted estimator) and preliminary test “PT” estimators are proposed, and their properties are investigated and compared with the unrestricted estimator “UE” of ρ 1 .

Keywords: autoregressive; homogeneity; pretest estimators; pooled estimator; asymptotic bias; asymptotic relative efficiency (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2024
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