Modeling volatility with Range-based Heterogeneous Autoregressive Conditional Heteroskedasticity model

In this paper a new ARCH-type volatility model is proposed. The Range-based Heterogeneous Autoregressive Conditional Heteroskedasticity (RHARCH) model draws inspiration from Heterogeneous Autoregressive Conditional Heteroskedasticity presented by Muller et al. (1995), but employs more efficient, range-based volatility estimators instead of simple squared returns in conditional variance equation. In the first part of this research range-based volatility estimators (such as Parkinson, or Garman-Klass estimators) are reviewed, followed by derivation of the RHARCH model. In the second part of this research the RHARCH model is compared with selected ARCH-type models with particular emphasis on forecasting accuracy. All models are estimated using data containing EURPLN spot rate quotation. Results show that RHARCH model often outperforms return-based models in terms of predictive abilities in both in-sample and out-of-sample periods. Also properties of standardized residuals are very encouraging in case of the RHARCH model.