• Journal of the Korean Mathematical Society
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• v.52 no.3
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• pp.503-522
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• 2015

In this paper, we consider the problem of testing for a parameter change in nonlinear time series models with GARCH type errors. We introduce two types of cumulative sum (CUSUM) tests: estimates-based and residual-based tests. It is shown that under regularity conditions, their limiting null distributions are the sup of independent Brownian bridges. A simulation study is conducted for illustration.

• 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.

• Korea Trade Review
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• v.47 no.3
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• pp.211-232
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• 2022

Due to the impact of the public health event COVID-19 epidemic, the Chinese futures market showed "Black Swan". This has brought the unpredictable into the economic environment with many commodities falling by the daily limit, while gold performed well and closed in the sunshine(Yan-Li and Rui Qian-Wang, 2020). Volatility is integral part of financial market. As an emerging market and a special precious metal, it is important to forecast return of gold futures price. This study selected data of the SHFE gold futures returns and conducted an empirical analysis based on the generalised autoregressive conditional heteroskedasticity (GARCH)-type model. Comparing the statistics of AIC, SC and H-QC, ARMA (12,9) model was selected as the best model. But serial correlation in the squared returns suggests conditional heteroskedasticity. Next part we established the autoregressive moving average ARMA-GARCH-type model to analysis whether Volatility Clustering and the leverage effect exist in the Chinese gold futures market. we consider three different distributions of innovation to explain fat-tailed features of financial returns. Additionally, the error degree and prediction results of different models were evaluated in terms of mean squared error (MSE), mean absolute error (MAE), Theil inequality coefficient(TIC) and root mean-squared error (RMSE). The results show that the ARMA(12,9)-TGARCH(2,2) model under Student's t-distribution outperforms other models when predicting the Chinese gold futures return series.

• The Korean Journal of Applied Statistics
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• v.28 no.3
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• pp.429-442
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• 2015

Volatility forecasting in financial markets is an important issue because it is directly related to the profit of return. The volatility is generally modeled as time-varying conditional heteroskedasticity. A generalized autoregressive conditional heteroskedastic (GARCH) model is often used for modeling; however, it is not suitable to reflect structural changes (such as a financial crisis or debt crisis) into the volatility. As a remedy, we introduce the Markov regime switching GARCH (MRS-GARCH) model. For the empirical example, we analyze and forecast the volatility of the daily Korea Composite Stock Price Index (KOSPI) data from January 4, 2000 to October 30, 2014. The result shows that the regime of low volatility persists with a leverage effect. We also observe that the performance of MRS-GARCH is superior to other GARCH models for in-sample fitting; in addition, it is also superior to other models for long-term forecasting in out-of-sample fitting. The MRS-GARCH model can be a good alternative to GARCH-type models because it can reflect financial market structural changes into modeling and volatility forecasting.

• Journal of the Korean Data and Information Science Society
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• v.28 no.3
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• pp.697-707
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• 2017

In this paper, we propose a modified GARCH(p, q)-X model which is obtained by adding the exogenous variables to the modified GARCH(p, q) process. Some limiting properties are shown under various stationary and nonstationary exogenous processes which are generated by another process independent of the noise process. The proposed model extends the GARCH(1, 1)-X model studied by Han (2015) to various GARCH(p, q)-type models such as GJR GARCH, asymptotic power GARCH and VGARCH combined with exogenous process. In comparison with GARCH(1, 1)-X, we expect that many stylized facts including long memory property of the financial time series can be explained effectively by modified GARCH(p, q) model combined with proper additional covariate.

• Journal of the Korean Data and Information Science Society
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• v.18 no.1
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• pp.11-16
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• 2007

Since the seminal work of Engle (1982), many researchers and practitioners have developed ARCH-type models to deal with volatility modelling, which, for instance, is crucial to perform the task of derivative pricing, measuring risk, and risk hedging. In this paper, we base the GARCH(1,1) model to analyze the KOSPI200 data, and perform the CUSUM test for detecting parameter changes in the GARCH model. It is shown that the data suffers from a parameter change.

• The Journal of Asian Finance, Economics and Business
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• v.7 no.4
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• pp.59-70
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• 2020

The purpose of this study is to construct the ACD model for the block trading volume duration. The ACD model based on the block trading volume duration is referred to as Volume ACD (VACD) in this study. By integrating with GARCH-type models, the VACD based GARCH type models, which include VACD-GARCH, VACD-IGARCH and VACD-FIGARCH models, are set up. This study selects Chunghwa Telecom (CHT) Inc., offering the America Depository Receipt (ADR) in NYSE, to investigate the block trading volume duration in Taiwanese equity market. The empirical results indicate that the long memory in volume duration series increases dependence at level of volatility clustering by VACD (2,1)-FIGARCH (3,d,1) model. Moreover, the VACD (2,1)-IGARCH (1,1) exhibits relatively better performance of prediction on capturing block trading volume duration. This volatility model is more appropriate in this study to portray the change of the CHT Inc. prices and provides more information about the volatility process for investment strategy, which can be a reference indicator of financial asset pricing, hedging strategy and risk management.

• Journal of the Korean Data and Information Science Society
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• v.20 no.2
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• pp.453-458
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• 2009

In this paper, we consider Jarque-Bera (JB) normality test for the innovations of ARMA-GARCH models. In financial applications, JB test based on the residuals are routinely used for the normality of ARMA-GARCH innovations without a justification. However, the validity of JB test should be justified in advance of the actual practice (Lee et al., 2009). Through the simulation study, it is found that the validity of JB test depends on the shape of test statistic. Specifically, when the constant term is involved in ARMA model, a certain type of residual based JB test produces severe size distortions.

• The Korean Journal of Applied Statistics
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• v.29 no.1
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• pp.1-12
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• 2016

Contrasted with the standard linear ARMA models, financial time series exhibits non-standard features such as fat-tails, non-normality, volatility clustering and asymmetries which are usually referred to as "stylized facts" in financial time series context (Terasvirta, 2009). We are accordingly led to ad hoc models (apart from ARMA) to accommodate stylized facts (Andersen et al., 2009). The paper aims to give a contemporary overview on financial and special time series models based on the recent literature and on the author's publications. Various models are illustrated including asymmetric models, integer valued models, multivariate models and high frequency models. Selected statistical issues on the models are discussed, bringing some perspectives to the future works in this area.

• The Korean Journal of Applied Statistics
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• v.34 no.4
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• pp.611-622
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• 2021

With a wide recognition that financial time series typically exhibits asymmetry patterns in volatility so called leverage effects, various asymmetric GARCH(1, 1) processes have been introduced to investigate asymmetric volatilities. A lot of researches have also been directed to non-stationary volatilities to deal with frequent high ups and downs in financial time series. This article is concerned with both asymmetric and non-stationary GARCH-type models. As a subsequent paper of Choi et al. (2020), we review various asymmetric and non-stationary GARCH(1, 1) processes, and in turn propose how to compare competing models using a parametric bootstrap methodology. As an illustration, Dow Jones Industrial Average (DJIA) is analyzed.