Structural change tests under heteroskedasticity: Joint estimation versus two‐steps methods

There has been a recent upsurge of interest in testing for structural changes in heteroskedastic time series, as changes in the variance invalidate the asymptotic distribution of conventional structural change tests. Several tests have been proposed that are robust to general form of heteroskedastic errors. The most popular use a two‐steps approach: first estimate the residuals assuming no changes in the regression coefficients; second, use the residuals to approximate the heteroskedastic asymptotic distribution or take an entire sample average to construct a test for which the variance process is averaged out. An alternative approach was proposed by Perron et al. (Perron et al. (2020). Quantitative Economics 11: 1019–1057) who provided a test for changes in the coefficients allowing for changes in the variance of the error term. We show that it transforms the variance profile into one that effectively has very little impact on the size of the test. With respect to the power properties, the two‐steps procedures can suffer from non‐monotonic power problems in dynamic models and in static models with a correction for serial correlation in the error. Most have power equals to size with zero‐mean regressors. Even when the two‐steps tests have power, it is generally lower than that of the latter test.