Real-Time Monitoring for Stock Return Predictability in Nonstationary Volatility Environments

Stock return predictability, should it exist, is likely to be episodic in nature. In order to exploit such pockets of predictability it is essential that they are rapidly detected, in real-time, as the nascent predictive regime emerges. This will typically entail the repeated (sequential) application of one-shot end-of-sample predictability statistics, updated as new data become available. Consequently, in addition to dealing with the usual inference problems caused by unknown regressor persistence and predictive regression endogeneity, one must also account for the multiple testing issues inherent in such monitoring procedures. In addition, stock returns and/or the predictors commonly used typically exhibit time-varying volatility and it is known that ignoring such data features can result in the spurious detection of predictability. We propose real-time monitoring procedures which take account of these issues. Our preferred monitoring strategy uses a CUSUM-type procedure based on a specific moment condition related to the predictive power of the putative predictor. We implement nonparametric adjustment methods to allow for the possibility of time-varying volatility which do not require the practitioner to assume any particular parametric model for volatility. Monte Carlo simulations confirm that our proposed detection procedures display well-controlled false positive rates across a range of feasible volatility paths coupled with good power to rapidly detect an emerging predictive episode. The empirical relevance of our proposed monitoring strategy is illustrated in a pseudo real-time monitoring exercise using a well-known dataset of S&P 500 returns.