• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.541-550
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• 2003

We consider the generalized autoregressive model with conditional heteroscedasticity process(GARCH). It is proved that if (equation omitted) β/sub i/ < 1, then there exists a unique invariant initial distribution for the Markov process emdedding the given GARCH process. Geometric ergodicity, functional central limit theorems, and a law of large numbers are also studied.

• Communications for Statistical Applications and Methods
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• v.24 no.5
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• pp.443-455
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• 2017

In this paper, we study ARCH(${\infty}$) models with either geometrically decaying coefficients or hyperbolically decaying coefficients. Most popular autoregressive conditional heteroscedasticity (ARCH)-type models such as various modified generalized ARCH (GARCH) (p, q), fractionally integrated GARCH (FIGARCH), and hyperbolic GARCH (HYGARCH). can be expressed as one of these cases. Sufficient conditions for $L_2$-near-epoch dependent (NED) property to hold are established and the functional central limit theorems for ARCH(${\infty}$) models are proved.

• Journal of Korea Water Resources Association
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• v.39 no.12 s.173
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• pp.997-1012
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• 2006

We have presented a nonparametric stochastic approach for the SOI(Southern Oscillation Index) series that used nonlinear methodology called Nonlinear AutoRegressive(NAR) based on conditional kernel density function and CAFPE(Corrected Asymptotic Final Prediction Error) lag selection. The fitted linear AR model represents heteroscedasticity, and besides, a BDS(Brock - Dechert - Sheinkman) statistics is rejected. Hence, we applied NAR model to the SOI series. We can identify the lags 1, 2 and 4 are appropriate one, and estimated conditional mean function. There is no autocorrelation of residuals in the Portmanteau Test. However, the null hypothesis of normality and no heteroscedasticity is rejected in the Jarque-Bera Test and ARCH-LM Test, respectively. Moreover, the lag selection for conditional standard deviation function with CAFPE provides lags 3, 8 and 9. As the results of conditional standard deviation analysis, all I.I.D assumptions of the residuals are accepted. Particularly, the BDS statistics is accepted at the 95% and 99% significance level. Finally, we split the SOI set into a sample for estimating themodel and a sample for out-of-sample prediction, that is, we conduct the one-step ahead forecasts for the last 97 values (15%). The NAR model shows a MSEP of 0.5464 that is 7% lower than those of the linear model. Hence, the relevance of the NAR model may be proved in these results, and the nonparametric NAR model is encouraging rather than a linear one to reflect the nonlinearity of SOI series.

• Communications for Statistical Applications and Methods
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• v.18 no.3
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• pp.319-331
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• 2011

In this paper, we propose automatic procedures for the model selection of various univariate time series data. Automatic model selection is important, especially in data mining with large number of time series, for example, the number (in thousands) of signals accessing a web server during a specific time period. Several methods have been proposed for automatic model selection of time series. However, most existing methods focus on linear time series models such as exponential smoothing and autoregressive integrated moving average(ARIMA) models. The key feature that distinguishes the proposed procedures from previous approaches is that the former can be used for both linear time series models and nonlinear time series models such as threshold autoregressive(TAR) models and autoregressive moving average-generalized autoregressive conditional heteroscedasticity(ARMA-GARCH) models. The proposed methods select a model from among the various models in the prediction error sense. We also provide an R package autots that implements the proposed automatic model selection procedures. In this paper, we illustrate these algorithms with the artificial and real data, and describe the implementation of the autots package for R.

• Communications for Statistical Applications and Methods
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• v.26 no.3
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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.

• Korean Journal of Agricultural Science
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• v.45 no.4
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• pp.859-870
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• 2018

Dried red peppers are a staple agricultural product used in Korean cuisine and as such, are an important aspect of agricultural producers' income. Correctly forecasting both their supply and demand situations and price is very important in terms of the producers' income and consumer price stability. The primary objective of this study was to compare the performance of time series forecasting models for dried red peppers in Korea. In this study, three models (an autoregressive model with exogenous variables [ARX], AR-exponential generalized autoregressive conditional heteroscedasticity [EGARCH], and ARX-EGARCH) are presented for forecasting the wholesale price of dried red peppers. As a result of the analysis, it was shown that the ARX model and ARX-EGARCH model, each of which adopt both the rolling window and the adding approach and use the agricultural cooperatives price as the exogenous variable, showed a better forecasting performance compared to the autoregressive model (AR)-EGARCH model. Based on the estimation methods and results, there was no significant difference in the accuracy of the estimation between the rolling window and adding approach. In the case of dried red peppers, there is limitation in building the price forecasting models with a market-structured approach. In this regard, estimating a forecasting model using only price data and identifying the forecast performance can be expected to complement the current pricing forecast model which relies on market shipments.

• Communications for Statistical Applications and Methods
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• v.13 no.3
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• pp.491-501
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• 2006

We consider a multiple change point model with autoregressive conditional heteroscedasticity (ARCH). The model assumes that all or the part of the parameters in the ARCH equation change over time. The occurrence of the change points is modelled as the discrete time Markov process with unknown transition probabilities. The model is estimated by Markov chain Monte Carlo methods based on the approach of Chib (1998). Simulation is performed using a variant of perfect sampling algorithm to achieve the accuracy and efficiency. We apply the proposed model to the simulated data for verifying the usefulness of the model.

• The Journal of Asian Finance, Economics and Business
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• v.7 no.11
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• pp.117-126
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• 2020

This paper is aimed to explore the co-movement capital market in Southeast Asia and analysis the correlation of conventional and Islamic Index in the regional and global equity. This research become necessary to represent the risk on the capital market and measure market performance, as investor considers the volatility before investing. The time series daily data use from April 2012 to April 2020 both conventional and Islamic stock index in Malaysia and Indonesia. This paper examines the dynamics of conditional volatilities and correlations between those markets by using Multivariate Generalized Autoregressive Conditional Heteroscedasticity (MGARCH). Our result shows that conventional or composite index in Malaysia less volatile than Islamic, but on the other hand, both drive correlation movement. The other output captures that Islamic Index in Indonesian capital market more gradual volatilities than the Composite Index that tends to be low in risk so that investors intend to keep the shares. Generally, the result shows a correlation in each country for conventional and the Islamic index. However, Internationally Indonesia and Malaysia composite and Islamic is low correlated. Regionally Indonesia's indices movement looks to be more correlated and it's similar to Malaysian Capital Market counterparts. In the global market distress condition, the diversification portfolio between Indonesia and Malaysia does not give many benefits.

• The Korean Journal of Applied Statistics
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• v.28 no.1
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• pp.115-122
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• 2015

This article is concerned with count time series taking values in non-negative integers. Along with the first order mean of the count time series, conditional variance (volatility) has recently been paid attention to and therefore various integer-valued GARCH(generalized autoregressive conditional heteroscedasticity) models have been suggested in the last decade. We introduce diverse integer-valued GARCH(INGARCH, for short) processes to count time series and a real data application is illustrated as a case study. In addition, zero inflated INGARCH models are discussed to accommodate zero-inflated count time series.

• ETRI Journal
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• v.35 no.5
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• pp.849-858
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• 2013

In this paper, we propose a new adaptive single model to track a maneuvering target with abrupt accelerations. We utilize the stochastic differential equation to model acceleration of a maneuvering target with stochastic volatility (SV). We assume the generalized autoregressive conditional heteroscedasticity (GARCH) process as the model for the tracking procedure of the SV. In the proposed scheme, to track a high maneuvering target, we modify the Kalman filtering by introducing a new GARCH model for estimating SV. The proposed tracking algorithm operates in both the non-maneuvering and maneuvering modes, and, unlike the traditional decision-based model, the maneuver detection procedure is eliminated. Furthermore, we stress that the improved performance using the GARCH acceleration model is due to properties inherent in GARCH modeling itself that comply with maneuvering target trajectory. Moreover, the computational complexity of this model is more efficient than that of traditional methods. Finally, the effectiveness and capabilities of our proposed strategy are demonstrated and validated through Monte Carlo simulation studies.