• Communications for Statistical Applications and Methods
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• 제13권2호
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• pp.343-358
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• 2006

The distributional properties of forecasts in an integer-valued time series model have not been discovered yet mainly because of the complexity arising from the binomial thinning operator. We propose two bootstrap methods to obtain nonparametric prediction intervals for an integer-valued autoregressive model : one accommodates the variation of estimating parameters and the other does not. Contrary to the results of the continuous ARMA model, we show that the latter is better than the former in forecasting the future values of the integer-valued autoregressive model.

• Communications for Statistical Applications and Methods
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• 제26권3호
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• pp.295-304
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• 2019

This article deals with threshold-asymmetric volatility models for over-dispersed and zero-inflated time series of count data. We introduce various threshold integer-valued autoregressive conditional heteroscedasticity (ARCH) models as incorporating over-dispersion and zero-inflation via conditional Poisson and negative binomial distributions. EM-algorithm is used to estimate parameters. The cholera data from Kolkata in India from 2006 to 2011 is analyzed as a real application. In order to construct the threshold-variable, both local constant mean which is time-varying and grand mean are adopted. It is noted via a data application that threshold model as an asymmetric version is useful in modelling count time series volatility.

• 응용통계연구
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• 제28권3호
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• pp.583-592
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• 2015

영-과잉(zero-inflation) 현상은 최근 계수(count) 시계열 분석의 주요토픽으로 다루어지고 있다. 본 논문에서는 영-과잉 계수 시계열의 변동성을 연구하고 있다. 기존의 정수형 모형인 INGARCH(integer valued GRACH) 모형에 조건부 포아송 및 조건부 음이항 분포를 사용하여 변동성에 영-과잉 현상을 추가하였다. 모수 추정 방법으로 EM알고리즘을 사용하였으며 국내 콜레라 발생건수에 적용시켜 보았다.

• 응용통계연구
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• 제28권1호
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• pp.115-122
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• 2015

본 연구에서는 정수값을 갖는 계수 시계열의 조건부 이차적률인 변동성(volatility)을 다루고 있다. 여러 가지 정수값 GARCH, 즉, INGARCH 모형들을 소개하고 계수 시계열인 국내 풍진발생건수에 적용시켜 보았다. 과산포(over-dispersion)와 영과잉(zero-inflation)현상을 계수 시계열의 변동성 분석 입장에서 살펴보았고 향후 분석 모형으로서 영과잉(zero-inflation) INGARCH 모형인 ZI-INGARCH 모형을 살펴보았다.

• Communications for Statistical Applications and Methods
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• 제25권1호
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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 Statistical Society
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• 제35권1호
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• pp.37-47
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• 2006

Recently, as a result of the growing interest in modeling stationary processes with discrete marginal distributions, several models for integer valued time series have been proposed in the literature. One of these models is the integer-valued autoregressive (INAR) models. However, when modeling with integer-valued autoregressive processes, the distributional properties of forecasts have been not yet discovered due to the difficulty in handling the Steutal Van Ham thinning operator 'o' (Steutal and van Ham, 1979). In this study, we derive the mean squared error of h-step-ahead prediction from a Poisson INAR(1) process, reflecting the effect of the variability of parameter estimates in the prediction mean squared error.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2005년도 추계 학술발표회 논문집
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• pp.159-165
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• 2005

Recently, as a result of the growing interest in modelling stationary processes with discrete marginal distributions, several models for integer valued time series have been proposed in the literature. One of theses models is the integer-valued autoregressive(INAR) models. However, when modelling with integer-valued autoregressive processes, there is not yet distributional properties of forecasts, since INAR process contain an accrued level of complexity in using the Steutal and Van Harn(1979) thinning operator 'o'. In this study, a manageable expression for the asymptotic mean square error of predicting more than one-step ahead from an estimated poisson INAR(1) model is derived. And, we present a bootstrap methods developed for the calculation of forecast interval limits of INAR(p) model. Extensive finite sample Monte Carlo experiments are carried out to compare the performance of the several bootstrap procedures.

• Communications for Statistical Applications and Methods
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• 제30권3호
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• pp.273-289
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• 2023

In this paper, we develop a new time series model for predicting IPO (initial public offering) data with non-negative integer value. The proposed model is based on integer-valued autoregressive (INAR) model with a Poisson thinning operator. Just as the heterogeneous autoregressive (HAR) model with daily, weekly and monthly averages in a form of cascade, the integer-valued heterogeneous autoregressive (INHAR) model is considered to reflect efficiently the long memory. The parameters of the INHAR model are estimated using the conditional least squares estimate and Yule-Walker estimate. Through simulations, bias and standard error are calculated to compare the performance of the estimates. Effects of model fitting to the Korea's IPO are evaluated using performance measures such as mean square error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE) etc. The results show that INHAR model provides better performance than traditional INAR model. The empirical analysis of the Korea's IPO indicates that our proposed model is efficient in forecasting monthly IPO volumes.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2002년도 추계 학술발표회 논문집
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• pp.265-272
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• 2002

An Integer-valued autoregressive integrated (INARI) model is introduced to eliminate stochastic trend and seasonality from time series of count data. This INARI extends the previous integer-valued ARMA model. We show that it is stationary and ergodic to establish asymptotic normality for conditional least squares estimator. Optimal estimating equations are used to reflect categorical and serial correlations arising from panel count data and variations arising from three random processes for obtaining observation into estimation. Under regularity conditions for martingale sequence, we show asymptotic normality for estimators from the estimating equations. Using cancer mortality data provided by the U.S. National Center for Health Statistics (NCHS), we apply our results to estimate the probability of cells classified by 4 causes of death and 6 age groups and to forecast death count of each cell. We also investigate impact of three random processes on estimation.

• Communications for Statistical Applications and Methods
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• 제27권2호
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• pp.177-187
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• 2020

This article is concerned with the issue of forecasting and evaluation of threshold-asymmetric volatility models for time series of count data. In particular, threshold integer-valued models with conditional Poisson and conditional negative binomial distributions are highlighted. Based on the parametric bootstrap method, some evaluation measures are discussed in terms of one-step ahead forecasting. A parametric bootstrap procedure is explained from which directional measure, magnitude measure and expected cost of misclassification are discussed to evaluate competing models. The cholera data in Bangladesh from 1988 to 2016 is analyzed as a real application.