This paper proposes a long memory stochastic range (LMSR) model to investigate the persistence of range-based volatility series. The latent variable in the LMSR model is derived from the established autoregressive fractionally integrated moving average process. To estimate the model parameters, there is no closed-form solution for the latent process. Hence, the parameters of the stochastic model are estimated by applying the quasi-maximum likelihood method via the Whittle approximation. A comprehensive simulation study assesses the method’s performance, with results showing that estimated parameters are close to true values and precision improves with longer simulated time series lengths. To demonstrate the applicability of the model, we conducted empirical studies based on four financial assets, and their volatilities are estimated directly using the range-based Parkinson (PK) volatility measure. The results show evidence of long memory in these volatility series using the rescaled range and Geweke-Porter-Hudak methods. We fit the resulting PK volatility estimates to the LMSR model and other competing volatility models, and their modelling performances are compared. Results indicate that all LMSR models outperform competitors according to the log-likelihood and Akaike information criterion as well as out-of-sample loss functions. Additionally, the estimated parameters of these LMSR models confirm the presence of long memory, while competing short memory models struggle to capture the persistent nature of volatility in financial markets.
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