• Communications for Statistical Applications and Methods
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• v.17 no.2
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• pp.255-261
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• 2010

A class of threshold-asymmetric GRACH(TGARCH, hereafter) models has been useful for explaining asymmetric volatilities in the field of financial time series. The cumulative impulse response function of a conditionally heteroscedastic time series often measures a degree of unstability in volatilities. In this article, a general form of the cumulative impulse response function of the TGARCH model is discussed. In particular, We present formula in their closed forms for the first two lower order models, viz., TGARCH(1, 1) and TGARCH(2, 2).

• 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.