We provide a comprehensive treatment for the problem of testing jointly for structural changes in both the regression coefficients and the variance of the errors in a single equation system involving stationary regressors. Our framework is quite general in that we allow for general mixing‐type regressors and the assumptions on the errors are quite mild. Their distribution can be nonnormal and conditional heteroskedasticity is permitted. Extensions to the case with serially correlated errors are also treated. We provide the required tools to address the following testing problems, among others: (a) testing for given numbers of changes in regression coefficients and variance of the errors; (b) testing for some unknown number of changes within some prespecified maximum; (c) testing for changes in variance (regression coefficients) allowing for a given number of changes in the regression coefficients (variance); (d) a sequential procedure to estimate the number of changes present. These testing problems are important for practical applications as witnessed by interests in macroeconomics and finance where documenting structural changes in the variability of shocks to simple autoregressions or vector autoregressive models have been a concern.

中文翻译：

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共同测试线性回归模型的误差方差和系数的结构变化

对于联合测试包含固定回归变量的单方程系统中回归系数和误差方差的结构变化，我们提供了一种综合测试的问题。我们的框架相当笼统，因为我们允许使用一般的混合型回归变量，并且对误差的假设相当温和。它们的分布可以是非正态的，并且允许有条件的异方差。具有序列相关错误的案例的扩展也将得到处理。我们提供解决以下测试问题所需的工具：（a）测试给定数量的回归系数变化和误差方差；（b）测试在预定的最大数量范围内的未知数量的变化；（c）测试方差的变化（回归系数），以考虑一定数量的回归系数的变化（方差）；（d）估计现有变更数量的顺序程序。这些测试问题对于实际应用非常重要，正如宏观经济学和金融学的兴趣所证明的那样，这些问题记录了对简单自回归或向量自回归模型的冲击变化的结构变化。