Autoregressive Moving Average Infinite Hidden Markov-Switching Models (original) (raw)
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Regime switching models, especially Markov switching models, are regarded as a promising way to capture nonlinearities in time series. Combining the elements of Markov switching models with full ARMA-GARCH models poses severe difficulties for the computation of parameter estimators. Existing methods can become completely unfeasible due to the full path dependence of such models. In this article we demonstrate how to overcome this problem. We formulate a full Markov switching ARMA-GARCH model and its Bayes estimator. This facilitates the use of Markov Chain Monte Carlo methods and allows us to develop an algorithm to compute the Bayes estimator of the regimes and parameters of our model. The approach is illustrated on simulated data and with returns from the New York Stock Exchange. Our model is then compared to other variants and proves clearly to be advantageous.
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This paper mainly discusses some regime-switching models and explore their usefulness in modeling the economic time series. In recent years, several time series models have been proposed which shape the idea of the existence of different regimes produced by a stochastic process. Especially, nonlinear time series models have gained more attention because linear time series models faced various limitations. The purpose of this study is to establish the methodology of the Self-Exciting Threshold Autoregressive (SETAR) model, Smooth Transition Autoregressive (STAR) model and Markov-Switching (MSW) model from parametric nonlinear time series models in the mean and to compare these models with each other through two financial data sets. For this purpose, some theoretical information on the subject models are given without going into too much detail. In the light of the obtained theoretical information, all models are modeled by using two financial data sets. The obtained models are compar...
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Bulletin of Economic Research, 2021
In this article, we develop one-and two-component Markov regime-switching conditional volatility models based on the intraday range and evaluate their performance in forecasting the daily volatility of the S&P 500 index. We compare the performance of the models with that of several well-established return-and range-based volatility models, namely EWMA, GARCH and FIGARCH models, the Markov Regime-Switching GARCH model of Klaassen (2002), the hybrid EWMA model of Harris and Yilmaz (2010), and the CARR model of Chou (2005). We evaluate the insample goodness of fit and out-of-sample forecast performance of the models using a comprehensive set of statistical and economic loss functions. To assess the statistical performance of the models, we use mean error metrics, directional predictive ability tests, forecast evaluation regressions, and pairwise and joint tests; and to appraise the economic performance of the models, we use value at risk coverage tests and risk management loss functions. We show that the proposed range-based Markov switching conditional volatility models produce more accurate out-ofsample forecasts, contain more information about true volatility and exhibit similar or better performance when used for the estimation of value at risk. Our results are robust to the choice of volatility proxy, estimation sample size, outof-sample evaluation period and alternative error distributions.
Time Varying Transition Probabilities for Markov Regime Switching Models
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We propose a new Markov switching model with time varying probabilities for the transitions. The novelty of our model is that the transition probabilities evolve over time by means of an observation driven model. The innovation of the time varying probability is generated by the score of the predictive likelihood function. We show how the model dynamics can be readily interpreted. We investigate the performance of the model in a Monte Carlo study and show that the model is successful in estimating a range of different dynamic patterns for unobserved regime switching probabilities. We also illustrate the new methodology in an empirical setting by studying the dynamic mean and variance behaviour of U.S. Industrial Production growth. We find empirical evidence of changes in the regime switching probabilities, with more persistence for high volatility regimes in the earlier part of the sample, and more persistence for low volatility regimes in the later part of the sample.
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