Long memory and regime switching in the stochastic volatility modelling
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Long memory and regime switching in the stochastic volatility modelling Yanlin Shi1 Accepted: 21 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract 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. Keywords Long memory · Stochastic volatility · Regime switching · MCMC
1 Introduction In time series analysis, unit root describes an I(d) sequence with d = 1, such that the process is non-stationary with the autoregressive correlation functions (ACFs) close to 1 for all lags. When d = 0, the time series is stationary, and its ACFs will decay geometrically. It is, however, possible for ACFs of a stationary process to decline more slowly, which is known as the hyperbolic decay. Among the existing literature, short-memory and long-memory persistences are used to describe the geometric and hyperbolic decays, respectively [see, for example, Diebold and Inoue (2001) and Perron and Qu (2010), among others]. In particular, for a first-moment sequence, Diebold and Inoue (2001) suggest that the long memory will exist for a stationary I(d) process, when 0 < d < 0.5. To illustrate those differences, Fig. 1a– c demonstrates the temporal plots and ACFs of simulated I(1), I(0) and I(d) (0 < d < 0.5) sequences, respectively.
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Yanlin Shi [email protected] Department of Actuarial Studies and Business Analytics, Macquarie University, Sydney, NSW 2109, Australia
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Annals of Operations Research
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Fig. 1 Illustrative examples: comparison of ACFs
In their influential research, Diebold and Inoue (2001) point out that when regime switching [see Zheng et al. (2019) for applications of regime-switching models, among others] is present, a short-memory process can also exhibit a long-memory feature. This is presented in Fig. 1d, where we uniformly add one to the second half of the same sample investigated in Fig. 1b. The ACFs of the new sequence, however, decay much more slowly than those of the original process and cannot be visually distinguished from the ACFs of Fig. 1c. This phenomenon is a
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