Forecasting the CBOE VIX and SKEW Indices Using Heterogeneous Autoregressive Models

We analyze the predictability of daily data on the CBOE  (Formula presented.)  and  (Formula presented.)  indices, used to capture the average level of risk-neutral risk and downside risk, respectively, as implied by S&P 500 index options. In particular, we use forecast models from the Heterogeneous Autoregressive ((Formula presented.)) class to test whether and how lagged values of the  (Formula presented.)  and of the  (Formula presented.)  may increase the forecasting power of  (Formula presented.)  for the  (Formula presented.)  and the  (Formula presented.). We find that a simple  (Formula presented.)  is very hard to beat in out-of-sample experiments aimed at forecasting the  (Formula presented.). In the case of the  (Formula presented.), the benchmarks (the random walk and an  (Formula presented.)) are clearly outperformed by  (Formula presented.)  models at all the forecast horizons considered and there is evidence that special definitions of the  (Formula presented.)  index based on put options data only yield superior forecasts at all horizons.