Long memory and regime switching in the stochastic volatility modelling

This paper studies the confusion between the long memory and regime switching in the second moment via the stochastic volatility (SV) methodology. An illustrative proposition is firstly presented with simulation evidence to demonstrate that spurious long memory can be caused by a Markov regime-switching SV (MRS-SV) process, when a long memory SV (LMSV) model is employed. To address this, an MRS-LMSV model is developed using a simulation-based optimization method, namely the Markov-Chain Monte Carlo algorithm. Via systematically constructed simulation studies, the proposed model can effectively distinguish between LMSV and MRS-SV processes with consistent estimators of the long-memory parameter. An empirical study of the S&P 500 daily returns is then conducted which demonstrates the superiority of the MRS-LMSV model over LMSV and MRS-SV counterparties. It is verified that significant long memory only exists in the high-volatility state. Important financial implications can be made to improve the risk management operations in practice.