This paper studies the properties of predictive regressions for asset returns in economic systems governed by persistent vector autoregressive dynamics. In particular, we allow for the state variables to be fractionally integrated, potentially of different orders, and for the returns to have a latent persistent conditional mean, whose memory is difficult to estimate consistently by standard techniques in finite samples. Moreover, the predictors may be endogenous and “imperfect.” In this setting, we develop a consistent local spectrum (LCM) estimation procedure, that delivers asymptotic Gaussian inference. Furthermore, we provide a new LCM-based estimator of the conditional mean persistence, that leverages biased regression slopes as well as new LCM-based tests for significance of (a subset of) the predictors, which are valid even without estimating the return persistence. Simulations illustrate the theoretical arguments. Finally, an empirical application to monthly S&P 500 return predictions provides evidence for a fractionally integrated conditional mean component. Our new LCM procedure and tools indicate significant predictive power for future returns stemming from key state variables such as the default spread and treasury interest rates.

本文研究了由持续向量自回归动力学控制的经济系统中资产回报预测回归的特性。特别是，我们允许对状态变量进行分数积分，可能具有不同的顺序，并且允许返回具有潜在的持久条件均值，其记忆难以通过有限样本中的标准技术一致地估计。此外，预测因素可能是内生的和“不完美的”。在这种情况下，我们开发了一种一致的局部频谱 (LCM) 估计程序，可提供渐近高斯推理。此外，我们提供了一种新的基于 LCM 的条件均值持久性估计器，它利用有偏回归斜率以及新的基于 LCM 的预测变量（子集）显着性检验，即使不估计返回持久性也是有效的。模拟说明了理论论点。最后，对标准普尔 500 指数月度回报预测的实证应用为分数积分条件均值分量提供了证据。我们新的 LCM 程序和工具表明，对来自关键状态变量（例如违约利差和国债利率）的未来回报具有显着的预测能力。