Why does the HAR model outperform GARCH for long-horizon vol forecasts?

HAR directly models the three time scales of market participants (daily traders, weekly fund managers, monthly investors) using observable realized vol. GARCH uses only the previous conditional variance, losing multi-scale information.

How is the weekly component RV_w computed?

RV_w(t) = (1/5) * sum_{k=0}^{4} RV(t-k), the trailing 5-day average of daily realized variance. Monthly component RV_m = (1/22) * sum_{k=0}^{21} RV(t-k).

HAR Model Heterogeneous Autoregressive Volatility

Forecast realized volatility using the HAR model: RV_t+1 = beta0 + beta_d*RV_t + beta_w*RV_w + beta_m*RV_m + epsilon. Daily, weekly, and monthly components capture multi-scale persistence.

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Frequently Asked Questions

Why does the HAR model outperform GARCH for long-horizon vol forecasts?

How is the weekly component RV_w computed?