Power and Size analysis of Co-integration tests in Conditional Heteroskedascity: A Monte Carlo Simulation

Abstract

This paper investigates the finite sample performance of power and size properties of several major co-integration tests using simulation analysis. These tests include; the co-integration Regression Durbin-Watson test (CRDW), Eagle-Granger test, Dicky Fuller unit root test with () statistics, Johansen likelihood ratio tests, and Phillips-Ouliaris test. Comparisons of tests are evaluated based on the proportion of rejects of the hypothesis of a no co-integration. This study answers the question of which co-integration test is better, particularly between the Eagle-Granger two-step test and the Johansen’s tests for co-integration, when the sets of parameters in models are persistence and spiky. The bivariate Generalized Autoregressive Conditional Heteroskedasticity (GARCH(1,1)) model with Gaussian innovations, is used in the data generating process (DGP). Our simulation results reveal that there is size distortion in the different co-integration test considered. The Eagle-Granger two-step test shows good robustness with respect to heteroskedasticity for the different sample sizes applied. However, the Johansen’s test for co-integration still proves to be powerful in capturing co-integration relationship, particularly for large sample when the co-integration innovations are Gaussian