Improved and extended end-of-sample instability tests using a feasible quasi-generalized least squares procedure

This paper extends the Andrews (2002, Econometrica 71, 1661-1694) and Andrews and Kim (2006, Journal of Business & Economic Statistics 24, 379-394) ordinary least squares-based end-of-sample instability tests for linear regression models. The author proposes to quasi-difference the data first using a consistent estimate of the sum of the autoregressive coefficients of the error process and then test for the end-of-sample instability. For the cointegration model, the feasible quasi-generalized least squares (FQGLS) version of the Andrews and Kim (2006) P test is considered and is shown, by simulations, to be more robust to serial correlation in the error process and to have power no less than Andrews and Kim's original test. For the linear time trend model, the FQGLS version of the Andrews (2002) S test is considered with the error process allowed to be nonstationary up to one unit root, and the new test is shown to be robust to potentially nonstationary serial correlation. A simulation study also shows that the finite-sample properties of the proposed test can be further improved when the Andrews (1993, Econometrica 61,139-165) or Andrews and Chen (1994, Journal of Business & Economic Statistics 12, 187-204) median unbiased estimate of the sum of the autoregressive coefficients is used.