Long memory tempered stochastic range model

This paper introduces a novel long memory tempered stochastic range (LMTSR) model to enhance volatility persistence modeling in asset prices. The LMTSR model integrates an autoregressive tempered fractionally integrated moving average process into the latent variable of the long memory stochastic range framework. Its key feature is the ability to capture long memory while ensuring stationarity when the long memory parameter exceeds 0.5, offering greater flexibility. Since no closed-form solution exists for estimating the latent process, model parameters are estimated using the quasi-maximum likelihood method via the Whittle approximation. An extensive simulation study indicates that the estimated parameters closely align with their true values. To demonstrate the model’s applicability, an empirical analysis based on the crude oil and S&P 500 data is conducted. The proposed model is fitted to range-based Parkinson volatility measures and contrasted with competing models by evaluating their in-sample model fit and out-of-sample forecasting performances. The in-sample results indicate that the LMTSR model outperforms its competitors in terms of log-likelihood and Akaike information criterion. For out-of-sample one-step-ahead forecasts, a simulation-based Sequential Monte Carlo approach is employed to track the evolution of latent variables over time. Out-of-sample loss functions further reveal that the LMTSR model delivers superior forecast accuracy.