The Markov-switching threshold BLGARCH model

R. Alraddadi; R. Alraddadi

doi:10.3934/math.2025842

AIMS Mathematics

2025, Volume 10, Issue 8: 18838-18860. doi: 10.3934/math.2025842

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Research article

The Markov-switching threshold BLGARCH model

R. Alraddadi ^,

Department of Mathematics and Statistics, College of Science in Yanbu, Taibah University, Madinah 46423, Saudi Arabia

Received: 27 March 2025 Revised: 17 June 2025 Accepted: 12 August 2025 Published: 20 August 2025
MSC : Primary 62M10; Secondary 62M05

This paper introduces a novel and enhanced class of Markov-switching threshold BLGARCH (MS-TBLG) models designed to better capture the intricate behavior of financial time series. By incorporating both a threshold mechanism and interaction effects between returns and their conditional volatility, the proposed framework significantly improves upon traditional Markov-switching BLGARCH (MS-BLG) models. This structure allows for a more flexible representation of regime-dependent volatility, particularly in modeling asymmetric effects such as the leverage effect—where negative and positive shocks have differing impacts across regimes. We established key conditions that guarantee the stationarity, causality, and ergodicity of the MS-TBLG process, and derived analytical expressions for its power covariance functions, taking the threshold effect into account. To estimate the model parameters efficiently, we developed a generalized method of moments (GMM) procedure specifically adapted to the complexity of Markov-switching dynamics. This approach utilizes moment conditions derived from the power-transformed squared process, ensuring consistent estimation despite the presence of unobserved regime shifts. The effectiveness and robustness of the estimation strategy were validated through extensive Monte Carlo simulations. Finally, the model's practical relevance was illustrated through an empirical application to oil price data, showcasing its effectiveness in capturing regime-switching behavior and complex volatility dynamics.
- GARCH model,
- bilinear model,
- Markov-switching model,
- GMM,
- stationarity,
- threshold effect
Citation: R. Alraddadi. The Markov-switching threshold BLGARCH model[J]. AIMS Mathematics, 2025, 10(8): 18838-18860. doi: 10.3934/math.2025842

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Abstract

This paper introduces a novel and enhanced class of Markov-switching threshold BLGARCH (MS-TBLG) models designed to better capture the intricate behavior of financial time series. By incorporating both a threshold mechanism and interaction effects between returns and their conditional volatility, the proposed framework significantly improves upon traditional Markov-switching BLGARCH (MS-BLG) models. This structure allows for a more flexible representation of regime-dependent volatility, particularly in modeling asymmetric effects such as the leverage effect—where negative and positive shocks have differing impacts across regimes. We established key conditions that guarantee the stationarity, causality, and ergodicity of the MS-TBLG process, and derived analytical expressions for its power covariance functions, taking the threshold effect into account. To estimate the model parameters efficiently, we developed a generalized method of moments (GMM) procedure specifically adapted to the complexity of Markov-switching dynamics. This approach utilizes moment conditions derived from the power-transformed squared process, ensuring consistent estimation despite the presence of unobserved regime shifts. The effectiveness and robustness of the estimation strategy were validated through extensive Monte Carlo simulations. Finally, the model's practical relevance was illustrated through an empirical application to oil price data, showcasing its effectiveness in capturing regime-switching behavior and complex volatility dynamics.

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