A permutation test for partial regression coefficients on first-order autocorrelation

Abstract

This dissertation proposes a permutation test and a permutation procedure for testing on partial regression coefficients from a multiple linear regression with first-order autocorrelation where the distribution of the error terms is not necessarily normal. The proposed permutation procedure can be directly conducted in the test without having to fit back to the model, which is not the same procedure as in previous permutation tests, and a proposed permutation test is considered based on a random permutation test. In addition, the asymptotic analysis of the proposed test can be obtained when errors are i.i.d. with mean zero and finite variance. The asymptotic distribution of , called the asymptotic chi-squared test, can be used to perform a significance test of partial regression coefficients. It was found that, for a small sample size (T=12), the proposed permutation method has the same type I error rate as the partial F-statistic and is not significantly different from the significance level , and has a higher power when compare with the other methods in the case where autocorrelation approached . However, with a moderate sample size (T=16, 20), the asymptotic chi-squared test is preferred (in terms of type I error and power of the test).