• Journal of the Korean Statistical Society
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• v.36 no.2
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• pp.183-200
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• 2007

We consider a nonlinear autoregressive moving average model with nonlinear GARCH errors, and find sufficient conditions for the existence of a strictly stationary solution of three related time series equations. We also consider a geometric ergodicity and functional central limit theorem for a nonlinear autoregressive model with nonlinear ARCH errors. The given model includes broad classes of nonlinear models. New results are obtained, and known results are shown to emerge as special cases.

• The Korean Journal of Applied Statistics
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• v.19 no.1
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• pp.33-41
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• 2006

In this paper, we analyse the volatilities in financial data such as stock prices and exchange rates in term of a class of nonlinear time series models. We compare the performance of Generalized Autoregressive Conditional Heteroscadastic(GARCH) , Integrated GARCH(IGARCH), Exponential GARCH(EGARCH) models by KOSPI (Korean stock Prices Index) data. The estimation for the parameters in the models was carried out by the ML methods.

• 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.

• Journal of the Korean Data and Information Science Society
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• v.21 no.5
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• pp.831-839
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• 2010

Least squares support vector machine (LS-SVM) is a kernel trick gaining a lot of popularities in the regression and classification problems. We use LS-SVM to propose a iterative algorithm for a nonlinear generalized autoregressive conditional heteroscedasticity model in the mean (GARCH-M) model to estimate the mean and the conditional volatility of stock market returns. The proposed method combines a weighted LS-SVM for the mean and unweighted LS-SVM for the conditional volatility. In this paper, we show that nonlinear GARCH-M models have a higher performance than the linear GARCH model and the linear GARCH-M model via real data estimations.

• Journal of the Korean Data and Information Science Society
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• v.18 no.1
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• pp.237-245
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• 2007

Nonlinear asymmetric time series models have the growing interest in econometrics and finance. Threshold model is one of the successful asymmetric model. We consider a smooth transition ARMA model which converges a.s. to a threshold ARMA model and show that the smooth transition ARMA model admits a stationary measure, provided a suitable condition on the coefficients of the autoregressive parts of the different regimes is satisfied. Stationarity of a smooth transition GARCH model is also obtained.

• The Korean Journal of Applied Statistics
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• v.36 no.4
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• pp.295-307
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• 2023

The heterogeneous autoregressive (HAR) model is a simple linear model that is commonly used to explain long memory in the realized volatility. However, as realized volatility has more complicated features such as conditional heteroscedasticity, leverage effect, and volatility clustering, it is necessary to extend the simple HAR model. Therefore, to better incorporate the stylized facts, we propose a threshold HAR model with GARCH errors, namely the THAR-GARCH model. That is, the THAR-GARCH model is a nonlinear model whose coefficients vary according to a threshold value, and the conditional heteroscedasticity is explained through the GARCH errors. Model parameters are estimated using an iterative weighted least squares estimation method. Our simulation study supports the consistency of the iterative estimation method. In addition, we show that the proposed THAR-GARCH model has better forecasting power by applying to the realized volatility of major 21 stock indices around the world.

• Journal of the Korean Data and Information Science Society
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• v.14 no.2
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• pp.265-274
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• 2003

Time series data are influenced by the external events such as holiday, strike, oil shock, and political change, so the external events cause a sudden change to the time series data. We regard the observation as outlier that occurred as a result of external events. In general, it is called intervention if we know the period and the reason of external events, and it makes an analyst difficult to establish a time series model. Therefore, it is important that we analyze the styles and effects of intervention. In this paper, we considered the linear time series model with invention and compared with nonlinear time series models such as ARCH, GARCH model and also we compared with the combination prediction method that Tong(1990) introduced. In the practical case study, we compared prediction power with RMSE among linear, nonlinear time series model with intervention and combination prediction method.

• Journal of the Korean Data and Information Science Society
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• v.21 no.3
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• pp.419-425
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• 2010

Kernel machine learning is gaining a lot of popularities in analyzing large or high dimensional nonlinear data. We use this technique to estimate a GARCH model for predicting the conditional volatility of stock market returns. GARCH models are usually estimated using maximum likelihood (ML) procedures, assuming that the data are normally distributed. In this paper, we show that GARCH models can be estimated using kernel machine learning and that kernel machine has a higher predicting ability than ML methods and support vector machine, when estimating volatility of financial time series data with fat tail.

• Communications for Statistical Applications and Methods
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• v.10 no.3
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• pp.931-954
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• 2003

It is widely recognized that economic time series involved not only the linearities but also the non-linearities. In this paper, when the economic time series data have the nonlinear characteristics we propose the forecasts method using combinations of both forecasts from linear and nonlinear models. In empirical study, we compare the forecasting performance of 4 exchange rates models(AR, GARCH, AR+GARCH, Bilinear model) and combination of these forecasts for dairly Won/Dollar exchange rates returns. The combination method is selected by the estimated individual forecast errors using Monte Carlo simulations. And this study shows that the combined forecasts using unrestricted least squares method is performed substantially better than any other combined forecasts or individual forecasts.

• Journal of Intelligence and Information Systems
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• v.16 no.2
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• pp.19-32
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• 2010

Volatility plays a central role in both academic and practical applications, especially in pricing financial derivative products and trading volatility strategies. This study presents a novel mechanism based on generalized autoregressive conditional heteroskedasticity (GARCH) models that is able to enhance the performance of intelligent volatility trading systems by predicting Korean stock market volatility more accurately. In particular, we embedded the concept of the volatility asymmetry documented widely in the literature into our model. The newly developed Korean stock market volatility index of KOSPI 200, VKOSPI, is used as a volatility proxy. It is the price of a linear portfolio of the KOSPI 200 index options and measures the effect of the expectations of dealers and option traders on stock market volatility for 30 calendar days. The KOSPI 200 index options market started in 1997 and has become the most actively traded market in the world. Its trading volume is more than 10 million contracts a day and records the highest of all the stock index option markets. Therefore, analyzing the VKOSPI has great importance in understanding volatility inherent in option prices and can afford some trading ideas for futures and option dealers. Use of the VKOSPI as volatility proxy avoids statistical estimation problems associated with other measures of volatility since the VKOSPI is model-free expected volatility of market participants calculated directly from the transacted option prices. This study estimates the symmetric and asymmetric GARCH models for the KOSPI 200 index from January 2003 to December 2006 by the maximum likelihood procedure. Asymmetric GARCH models include GJR-GARCH model of Glosten, Jagannathan and Runke, exponential GARCH model of Nelson and power autoregressive conditional heteroskedasticity (ARCH) of Ding, Granger and Engle. Symmetric GARCH model indicates basic GARCH (1, 1). Tomorrow's forecasted value and change direction of stock market volatility are obtained by recursive GARCH specifications from January 2007 to December 2009 and are compared with the VKOSPI. Empirical results indicate that negative unanticipated returns increase volatility more than positive return shocks of equal magnitude decrease volatility, indicating the existence of volatility asymmetry in the Korean stock market. The point value and change direction of tomorrow VKOSPI are estimated and forecasted by GARCH models. Volatility trading system is developed using the forecasted change direction of the VKOSPI, that is, if tomorrow VKOSPI is expected to rise, a long straddle or strangle position is established. A short straddle or strangle position is taken if VKOSPI is expected to fall tomorrow. Total profit is calculated as the cumulative sum of the VKOSPI percentage change. If forecasted direction is correct, the absolute value of the VKOSPI percentage changes is added to trading profit. It is subtracted from the trading profit if forecasted direction is not correct. For the in-sample period, the power ARCH model best fits in a statistical metric, Mean Squared Prediction Error (MSPE), and the exponential GARCH model shows the highest Mean Correct Prediction (MCP). The power ARCH model best fits also for the out-of-sample period and provides the highest probability for the VKOSPI change direction tomorrow. Generally, the power ARCH model shows the best fit for the VKOSPI. All the GARCH models provide trading profits for volatility trading system and the exponential GARCH model shows the best performance, annual profit of 197.56%, during the in-sample period. The GARCH models present trading profits during the out-of-sample period except for the exponential GARCH model. During the out-of-sample period, the power ARCH model shows the largest annual trading profit of 38%. The volatility clustering and asymmetry found in this research are the reflection of volatility non-linearity. This further suggests that combining the asymmetric GARCH models and artificial neural networks can significantly enhance the performance of the suggested volatility trading system, since artificial neural networks have been shown to effectively model nonlinear relationships.