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In this paper we model regimes and long memory in the dynamics of realized volatilities of intraday ETF and stock returns. We estimate threshold fractionally integrated (TARFIMA) models using Bayesian Markov Chain Monte Carlo (MCMC) algorithms with efficient jump. We also introduce a test based on posterior distributions of the mean squared forecast errors for model selection. Our findings are that the TARFIMA model that accounts for a different degree of long memory, persistence and variance in two regimes outperforms ARFIMA and other models using 5 day forecasts.

Regimes and long memory in realized volatility