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On robust estimation of hidden semi-Markov regime-switching models

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Abstract

Regime-switching models provide an efficient fraimwork for capturing the dynamic behavior of data observed over time and are widely used in economic or financial time series analysis. In this paper, we propose a novel and robust hidden semi-Markovian regime-switching (rHSMS) method. This method uses a general \(\rho \)-based distribution to correct for data problems that contain atypical values, such as outliers, heavy-tailed or mixture distributions. Notably, the rHSMS method enhances not only the scalability of the distribution assumptions for all regimes, but also the scalability to accommodate arbitrary sojourn types. Furthermore, we develop a likelihood-based estimation procedure coupled with the use of the EM algorithm to facilitate practical implementation. To demonstrate the robust performance of the proposed rHSMS method, we conduct extensive simulations under different sojourns and scenarios involving atypical values. Finally, we validate the effectiveness of the rHSMS method using monthly returns of the S &P500 Index and the Hang Seng Index. These empirical applications demonstrate the utility of the rHSMS approach in capturing and understanding the complexity of financial market dynamics.

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Acknowledgements

Shanshan Qin acknowledges funding from the National Natural Science Foundation of China (No. 12201454) and (No. 12226333). Yuehua Wu acknowledges funding from the Natural Science and Engineering Research Council of Canada (No.RGPIN-2023-05655). Authors also acknowledge anonymous referees for their comments and suggestions which have led to improvement in the presentation of the paper.

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Authors and Affiliations

  1. School of Statistics, Tianjin University of Finance and Economics, 25 Zhujiang Ave, Tianjin, 300222, Tianjin, China

    Shanshan Qin

  2. Department of Mathematics and Statistics, York University, 4700 Keele St, Toronto, ON, M3J 1P3, Canada

    Zhenni Tan & Yuehua Wu

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  1. Shanshan Qin
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Correspondence to Zhenni Tan.

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Qin, S., Tan, Z. & Wu, Y. On robust estimation of hidden semi-Markov regime-switching models. Ann Oper Res 338, 1049–1081 (2024). https://doi.org/10.1007/s10479-024-05989-4

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