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.

中文翻译：

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异方差下的结构变化检验：联合估计与两步法

最近对异方差时间序列中的结构变化进行测试的兴趣高涨，因为方差的变化使传统结构变化测试的渐近分布无效。已经提出了几个对一般形式的异方差误差具有鲁棒性的测试。最流行的使用两步法：首先估计残差，假设回归系数没有变化；其次，使用残差逼近异方差渐近分布或取整个样本平均来构建方差过程平均的检验。Perron等人提出了一种替代方法。(Perron et al. (2020).数量经济学 11: 1019–1057)，他们对系数变化进行了检验，允许误差项的方差发生变化。我们表明，它将方差分布转换为对测试规模几乎没有影响的方差分布。关于功率属性，两步过程可能会遇到动态模型和静态模型中的非单调功率问题，并校正误差中的序列相关性。大多数具有等于零均值回归变量的大小。即使在两步测试有威力的情况下，也普遍低于后一种测试。