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Artificial regression testing in the GARCH-in-mean model

机译：GARCH均值模型中的人工回归测试

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摘要

The issue of finite-sample inference in Generalised Autoregressive Conditional Heteroskedasticity (GARCH)-like models has seldom been explored in the theoretical literature, although its potential relevance for practitioners is obvious. In some cases, asymptotic theory may provide a very poor approximation to the actual distribution of the estimators in finite samples. The aim of this paper is to propose the application of the so-called double length regressions (DLR) to GARCH-in-mean models for inferential purposes. As an example, we focus on the issue of Lagrange Multiplier tests on the risk premium parameter. Simulation evidence suggests that DLR-based Lagrange Multiplier (LM) test statistics provide a much better testing framework than the more commonly used LM tests based on the outer product of gradients (OPG) in terms of actual test size, especially when the GARCH process exhibits high persistence in volatility. This result is consistent with previous studies on the subject.
机译：尽管在广义的自回归条件异方差（GARCH）模型中，有限样本推断的问题在理论文献中很少被探讨，尽管它对从业者的潜在意义是显而易见的。在某些情况下，渐近理论可能无法对有限样本中估计量的实际分布提供非常差的近似值。本文的目的是为推理目的将所谓的双长度回归（DLR）应用于均值GARCH模型。例如，我们重点研究风险溢价参数的拉格朗日乘数检验问题。仿真证据表明，基于DLR的拉格朗日乘数（LM）测试统计数据提供了比基于梯度外部乘积（OPG）的更常用LM测试更好的测试框架，尤其是在GARCH流程显示时高度持续的波动性。该结果与先前对该主题的研究一致。

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