Forecasting oil and stock returns with a Qual VAR using over 150 years of data

The extant literature suggests that oil price, stock price and economic activity are all endogenous and the linkages between these variables are nonlinear. Against this backdrop, the objective of this paper is to use a Qualitative Vector Autoregressive (Qual VAR) to forecast (West Texas Intermediate) oil and (S&P500) stock returns over a monthly period of 1884:09 to 2015:08, using an in-sample period of 1859:10-1884:08. Given that there is no data on economic activity at monthly frequency dating as far back as 1859:09, we measure the same using the NBER recession dummies, which in turn, can be easily accommodated in a Qual VAR as an endogenous variable. In addition, the Qual VAR is inherently a nonlinear model as it allows the oil and stock returns to behave as nonlinear functions of their own past values around business cycle turning points. Our results show that, for both oil and stock returns, the Qual VAR model outperforms the random walk model (in a statistically significant way) at all the forecasting horizons considered, i.e., one- to twelve-months-ahead. In addition, the Qual VAR model, also outperforms the AR and VAR models (in a statistically significant manner) at long-run horizons for oil returns, and short- to medium-run horizons for stock returns