Improved Tests for the First-Order Autoregressive Model With Heteroscedasticity

Abstract

In the first-order autoregressive model with nonconstant variance, likelihood ratio tests, score tests and modified likelihood ratio tests are derived to test each of the following hypotheses: (i) independence and homoscedasticity, (ii) independence, and (iii) homoscedasticity. Monte Carlo studies show that likelihood ratio tests can be very anticonservative, score tests are conservative and modified likelihood ratio tests are reliable and powerful tests. In addition, modified likelihood ratio tests for testing hypotheses (ii) and (iii) are robust in the presence of heteroscedasticity and autocorrelation, respectively.