• Communications for Statistical Applications and Methods
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• v.25 no.1
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• pp.29-42
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• 2018

We combine the integer-valued GARCH(1, 1) model with a generalized regime-switching model to propose a dynamic count time series model. Our model adopts Markov-chains with time-varying dependent transition probabilities to model dynamic count time series called the generalized regime-switching integer-valued GARCH(1, 1) (GRS-INGARCH(1, 1)) models. We derive a recursive formula of the conditional probability of the regime in the Markov-chain given the past information, in terms of transition probabilities of the Markov-chain and the Poisson parameters of the INGARCH(1, 1) process. In addition, we also study the forecasting of the Poisson parameter as well as the cumulative impulse response function of the model, which is a measure for the persistence of volatility. A Monte-Carlo simulation is conducted to see the performances of volatility forecasting and behaviors of cumulative impulse response coefficients as well as conditional maximum likelihood estimation; consequently, a real data application is given.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.4
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• pp.429-441
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• 2015

We study optimal consumption/investment and life insurance purchase rules for a wage earner with mortality risk under regime-switching financial market conditions, in a continuous time-horizon. We apply the Markov chain approximation method and suggest an efficient algorithm using parallel computing to solve the simultaneous Hamilton-Jaccobi-Bellman equations arising from the optimization problem. We provide numerical results under the utility functions of the constant relative risk aversion type, with which we illustrate the effects of regime switching on the optimal policies by comparing them with those in the absence of regime switching.

• The Korean Journal of Applied Statistics
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• v.27 no.6
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• pp.1049-1068
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• 2014

Autoregressive models are used to analyze an univariate time series data; however, these methods can be inappropriate when a structural break appears in a time series since they assume that a trend is consistent. Threshold autoregressive models (popular regime-switching models) have been proposed to address this problem. Recently, the models have been extended to two regime-switching models with delay parameter. We discuss two regime-switching threshold autoregressive models from a Bayesian point of view. For a Bayesian analysis, we consider a parametric threshold autoregressive model and a nonparametric threshold autoregressive model using Dirichlet process prior. The posterior distributions are derived and the posterior inferences is performed via Markov chain Monte Carlo method and based on two Bayesian threshold autoregressive models. We present a simulation study to compare the performance of the models. We also apply models to gross domestic product data of U.S.A and South Korea.