Stock returns predictability with unstable predictors

We re-examine predictability of US stock returns. Theoretically well-founded models predict that stationary combinations of I(1) variables such as the dividend or earnings to price ratios or the consumption/asset/income relationship often known as CAY may predict returns. However, there is evidence that these relationships are unstable, and that allowing for discrete shifts in the unconditional mean (location shifts) can lead to greater predictability. It is unclear why there should be a small number of discrete shifts and we allow for more general instability in the predictors, characterised by smooth variation variation, using a method introduced by Giraitis, Kapetanios and Yates. This can remove persistent components from observed time series, that may otherwise account for the presence of near unit root type behaviour. Our methodology may therefore be seen as an alternative to the widely used IVX methods where there is strong persistence in the predictor. We apply this to the three predictors mentioned above in a sample from 1952 to 2019 (including the financial crisis but excluding the Covid pandemic) and find that modelling smooth instability improves predictability and forecasting performance and tends to outperform discrete location shifts, whether identified by in-sample Bai-Perron tests or Markov-switching models.