A cusum test in the linear regression model with serially correlated disturbances

This paper considers a modified CUSUM test, suggested by Dufour (1982) for parameter instability and structural change with an unknown change point in a linear model with serially correlated disturbances, in which a preliminary estimate of the autoregressive coefficient for the error process is obtained, and used to transform the data. Then the standard CUSUM statistic is calculated on the transformed data. This paper derives the asymptotic distribution of the modified CUSUM test. We show that the modified CUSUM test retains its asymptotic significance level, i.e., the modified CUSUM test has the same asymptotic distribution as the CUSUM test with serially uncorrelated errors. Monte Carlo results suggest the performance of the standard CUSUM is quite disappointing, i.e., the empirical size of the test is highly distorted. This suggests that care must be taken when applying tests for structural change to serially correlated data. The results also indicated that the modified CUSUM and the Dufour tests are essentially interchangeable for a lagged dependent variable and for an AR(1) serial correlation, but there is no guarantee that this result is robust for higher order serial correlation.