Preliminary Test Estimation for Parallel 2-Sampling in Autoregressive Model

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 ρ1 and ρ2. Furthermore, we are interested in estimating ρ1 under uncertain and weak prior information about the possible equality of ρ1 and ρ2, 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 ρ1.