Coherent Forecasting of Realized Volatility

The QLIKE loss function is the stylized favorite of the literature on volatility forecasting when it comes to out‐of‐sample evaluation and the state of the art model for realized volatility (RV) forecasting is the HAR model, which minimizes the squared error loss for in‐sample estimation of the parameters. An obvious, but rarely implemented progression from the classical HAR model is to align the loss function used for out‐of‐sample forecast evaluation and in‐sample parameter estimation. While the MSE and QLIKE should result in the same solution asymptotically if the model is correctly specified, this empirical work reveals massive forecast performance gains from a HAR model that is directly estimated using the QLIKE loss (henceforth qlikeHAR). Especially, if the forecast performance is evaluated using the QLIKE loss, the qlikeHAR results in significantly better out‐of‐sample forecasting performance relative to the classical mseHAR.