Consistent Inference for Predictive Regressions in Persistent Economic Systems
Consistent Inference for Predictive Regressions in Persistent Economic Systems
复制标题
持久经济系统中预测回归的一致推理
DOI：
10.2139/ssrn.3359946
复制
发表时间：
2019
期刊：
影响因子：
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通讯作者：
R. T. Varneskov
中科院分区：
文献类型：
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作者：
T. Andersen;R. T. Varneskov
摘要本文研究了状态变量为持续向量自回归动态的经济系统中的标准预测回归。特别是，所有的变量或一个子集可以分数积分，这会导致虚假的回归问题。我们提出了一个新的推理和测试程序-本地speCtruM（LCM）的方法-联合显着的回归，这是强大的对具有不同的整合顺序的变量，并保持有效，无论预测是否显着，如果他们是，他们是否诱导协整。具体而言，LCM过程是基于分数滤波和频带频谱回归使用一组适当选择的频率坐标。与现有的方法相反，我们建立了一个统一的高斯极限理论和一个标准的χ 2分布检验统计量。使用LCM推理和测试技术，我们探索了预测回归的实现回报变化。标准最小二乘推断表明，流行的金融和宏观经济变量传递了有关未来回报波动的有价值的信息。相比之下，我们发现没有显着的证据，使用我们强大的LCM程序。如果说有什么不同的话，那就是我们的测试支持了一个反向因果链，即金融波动性的上升早于关键宏观经济变量的不利创新。模拟来说明有限样本推理的理论参数的相关性。
Abstract This paper studies standard predictive regressions in economic systems governed by persistent vector autoregressive dynamics for the state variables. In particular, all – or a subset – of the variables may be fractionally integrated, which induces a spurious regression problem. We propose a new inference and testing procedure – the Local speCtruM (LCM) approach – for joint significance of the regressors, that is robust against the variables having different integration orders and remains valid regardless of whether predictors are significant and, if they are, whether they induce cointegration. Specifically, the LCM procedure is based on fractional filtering and band spectrum regression using a suitably selected set of frequency ordinates. Contrary to existing procedures, we establish a uniform Gaussian limit theory and a standard χ 2 -distributed test statistic. Using the LCM inference and testing techniques, we explore predictive regressions for the realized return variation. Standard least squares inference indicates that popular financial and macroeconomic variables convey valuable information about future return volatility. In contrast, we find no significant evidence using our robust LCM procedure. If anything, our tests support a reverse chain of causality, with rising financial volatility predating adverse innovations to key macroeconomic variables. Simulations are employed to illustrate the relevance of the theoretical arguments for finite-sample inference.