Are combination forecasts of S&P 500 volatility statistically superior?

ARFIMA(1,d,O) case reveals that volatility exhibits long memory properties.

In order to generate model based volatility forecasts which capture the in-
formation available at time t efficiently, the volatility models were reestimated
for time-step t using data from t — 999 to t. The resulting parameter values
were then used to generate 22 day-ahead volatility forecasts (t + 1 → t + 22),
this time horizon is used for comparability with the VIX IV forecast. The first
forecast period covers the trading period from 13 December 1993 to 12 January
1994. For subsequent forecasts the model parameters were reestimated using a
sliding estimation window of 1OOO observations. The last forecast period covers
18 September 2OO3 to 17 October 2OO3, leaving 246O forecasts.

3.2 Combining forecasts

Two strategies have been employed to construct combination forecasts. The
simplest, and most naïve approach sets the combinations to be the mean of the
constituent forecasts, thus an equally weighted combination of each forecast.

The alternative is to utilise the regression combination approach discussed
in Clements and Hendry (1998) where the combination weights are derived from
the following regression,

^rvt+22 = ɑo ⁺ ɑi ft ^{+ s}2 ^ft ⁺ ∙∙∙ ^{+ a}n ft ^{+ e}t            ⁽⁷⁾

where RV_t∖₂₂ is the target volatility, the average RV over the 22 day forecast
horizon (t +1 to t + 22) and f_t^z, г = 1, 2, ..., n are n different forecasts of average
volatility (t + 1 to t + 22) formed at time t to be included in the combination.
The resulting combination forecast is then given by

ft = So + Si ft¹ + ¾ ft² + ∙∙∙ + a_n ft^ra                  (8)

1O

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