Modelling 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, pp. 213–239), but employs more efficient, range‑based volatility estimators instead of simple squared returns in a 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 with a maximum likelihood method 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 the case of the RHARCH model.