We introduce a set of test statistics for assessing the presence of regimes in out of sample forecast errors produced by recursively estimated linear predictive regressions that can accommodate multiple highly persistent predictors. Our test statistics are designed to be robust to the chosen starting window size and are shown to be both consistent and locally powerful. Their limiting null distributions are also free of nuisance parameters and hence robust to the degree of persistence of the predictors. Our methods are subsequently applied to the predictability of the value premium whose dynamics are shown to be characterized by state dependence.

中文翻译：

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通过预测回归发现样本误差之外的情况*

我们引入了一组测试统计信息，用于评估由递归估计的线性预测回归所产生的样本预测误差中制度的存在，这些误差可以容纳多个高度持久的预测因素。我们的测试统计信息旨在对所选的起始窗口大小具有鲁棒性，并被证明具有一致性和局部强大性。它们的有限零分布也没有干扰参数，因此对预测变量的持久性具有鲁棒性。我们的方法随后应用于价值溢价的可预测性，其价值表现为具有状态依赖性。