On double hysteretic heteroskedastic model |
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Authors: | Cathy WS Chen Buu-Chau Truong |
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Institution: | 1. Department of Statistics, Feng Chia University, Taichung, Taiwanchenws@mail.fcu.edu.tw;3. Department of Statistics, Feng Chia University, Taichung, Taiwan;4. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam |
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Abstract: | ABSTRACTThis paper proposes a hysteretic autoregressive model with GARCH specification and a skew Student's t-error distribution for financial time series. With an integrated hysteresis zone, this model allows both the conditional mean and conditional volatility switching in a regime to be delayed when the hysteresis variable lies in a hysteresis zone. We perform Bayesian estimation via an adaptive Markov Chain Monte Carlo sampling scheme. The proposed Bayesian method allows simultaneous inferences for all unknown parameters, including threshold values and a delay parameter. To implement model selection, we propose a numerical approximation of the marginal likelihoods to posterior odds. The proposed methodology is illustrated using simulation studies and two major Asia stock basis series. We conduct a model comparison for variant hysteresis and threshold GARCH models based on the posterior odds ratios, finding strong evidence of the hysteretic effect and some asymmetric heavy-tailness. Versus multi-regime threshold GARCH models, this new collection of models is more suitable to describe real data sets. Finally, we employ Bayesian forecasting methods in a Value-at-Risk study of the return series. |
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Keywords: | Asymmetry Bayesian methods hysteresis Markov chain Monte Carlo model selection posterior odds ratio value-at-risk skew Student's t-distribution threshold autoregressive model |
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