Forecast combination puzzle in the HAR model

The heterogeneous autoregressive (HAR) model has become the benchmark model for predicting realized volatility, given its simplicity and consistent empirical performance. Many modifications and extensions to the original model have been proposed that often only provide incremental forecast improvements. In this paper, we take a step back and view the HAR model as a forecast combination that combines three predictors: previous day realization (or random walk forecast), previous week average, and previous month average. When applying the ordinary least squares (OLS) to combine the predictors, the HAR model uses optimal weights that are known to be problematic in the forecast combination literature. In fact, an average of simpler HAR‐style models, and a simple average forecast often outperforms the optimal combination in many empirical applications. We investigate the performance of these simple combination forecasts for the realized volatility of the Dow Jones Industrial Average equity index, and a sample of individual constituent stocks, as well as across a range of other assets, commodities, exchange rates, and a range of global equity market indices. In all cases, we find dramatic improvements in forecast accuracy across all horizons and different time periods. The combinations also perform well relative to the logarithmic form of the HAR model and when using a volatility timing strategy in portfolio allocation. Thisis the first time the forecast combination puzzle is identified in this context.