• 대한수학회보
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• 제43권4호
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• pp.813-820
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• 2006

We consider a MAR model with ARCH type conditional heteroscedasticity. MAR-ARCH model can be derived as a smoothed version of the double threshold AR-ARCH model by adding a random error to the threshold parameters. Easy to check sufficient conditions for strict stationarity, ${\beta}-mixing$ property and existence of moments of the model are given via Markovian representation technique.

• Communications for Statistical Applications and Methods
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• 제22권5호
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• pp.463-473
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• 2015

We consider a nonparametric AR(1) model with nonparametric ARCH(1) errors. In order to estimate the unknown function of the ARCH part, we apply the stationary bootstrap procedure, which is characterized by geometrically distributed random length of bootstrap blocks and has the advantage of capturing the dependence structure of the original data. The proposed method is composed of four steps: the first step estimates the AR part by a typical kernel smoothing to calculate AR residuals, the second step estimates the ARCH part via the Nadaraya-Watson kernel from the AR residuals to compute ARCH residuals, the third step applies the stationary bootstrap procedure to the ARCH residuals, and the fourth step defines the stationary bootstrapped Nadaraya-Watson estimator for the ARCH function with the stationary bootstrapped residuals. We prove the asymptotic validity of the stationary bootstrap estimator for the unknown ARCH function by showing the same limiting distribution as the Nadaraya-Watson estimator in the second step.

• Communications for Statistical Applications and Methods
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• 제11권2호
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• pp.323-327
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• 2004

In this paper, we investigate the limiting distribution of the Ljung-Box test statistic in the unit root AR models with ARCH errors. We show that the limiting distribution is approximately chi-square distribution with the degrees of freedom only depending on the number of autocorrelation lags appearing in the test. Some simulation results are provided for illustration.

• 대한수학회논문집
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• 제17권2호
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• pp.309-319
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• 2002

We consider the nonlinear autoregressive model with nonlinear ARCH errors, and find sufficient conditions for the existence of a strictly stationary process. New results are obtained, and known results are shown to emerge as special oases.

• 대한수학회지
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• 제41권2호
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• pp.309-318
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• 2004

We consider a nonlinear AR-ARCH type process subject to Markov-switching and give sufficient conditions for geometric ergodicity of the process. Existence of moments is also obtained.

• Journal of the Korean Statistical Society
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• 제32권2호
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• pp.193-202
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• 2003

We consider a double threshold AR-ARCH type process and give sufficient conditions under which the higher-order moments exist. Geometric ergodicity and strict stationarity are also studied.

• 부동산연구
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• 제27권3호
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• pp.41-50
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• 2017

변동성 모형을 이용한 국내의 주택가격에 대한 기존의 연구에서는 변동성모형을 어떻게 주택시장분석에 적용할 수 있는지를 보여주고 있지만 최근 국내의 지역주택시장들에 나타나는 유의미한 변화를 반영하는데는 한계가 존재할 수 밖에 없다. 본 연구에서는 변동성모형을 적용하여 전국의 각 지역별 주택시장을 분석하고 이를 통해 미래의 지역별 주택시장의 가격변동을 실제적으로 예측하였다. AR(1)-ARCH(1), AR(1)-GARCH(1,1), AR(1)-EGARCH(1,1,1) 모형을 통하여 지역주택시장에 ARCH 및 GARCH효과가 존재하는 것을 확인하였다. 그리고 각 지역의 예측력을 비교하여 지역별 최적예측모형을 선정하였으며, 이러한 지역별 최적모형의 선정이 실제적으로 어떻게 이용될 수 있는지를 보여주기 위하여 2017년 하반기의 각 지역주택시장의 가격변동을 선정된 지역별 최적모형을 이용하여 예측하였다.

• Journal of the Korean Data and Information Science Society
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• 제15권4호
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• pp.783-791
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• 2004

In this paper we review recent developments in nonlinear time series modeling on both conditional mean and conditional variance. Traditional linear model in conditional mean is referred to as ARMA(autoregressive moving average) process investigated by Box and Jenkins(1976). Nonlinear mean models such as threshold, exponential and random coefficient models are reviewed and their characteristics are explained. In terms of conditional variances, ARCH(autoregressive conditional heteroscedasticity) class is considered as typical linear models. As nonlinear variants of ARCH, diverse nonlinear models appearing in recent literature including threshold ARCH, beta-ARCH and Box-Cox ARCH models are remarked. Also, a class of unified nonlinear models are considered and parameter estimation for that class is briefly discussed.

• 응용통계연구
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• 제34권4호
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• pp.623-632
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• 2021

본 연구에서는 여러가지 시계열 모형 중 평활법(가법계절지수, 승법계절지수), 계절 ARIMA 모형, ARARCH 그리고 AR-GARCH 회귀모형을 이용하여 최대 전력수요를 예측하는 방법을 연구하였다. 이 때 가중 평균모형으로 추세를 갖는 시계열 모형과 온도에 대한 회귀 모형을 적절한 가중치로 예측 정확도를 높이는 방법도 연구하였다. 결과적으로 AR-GARCH 회귀모형으로 예측하는 것이 가중 우수함을 보였다.

• Journal of Information Technology Applications and Management
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• 제25권4호
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• pp.157-169
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• 2018

The purpose of this study was to examine the volatility of bitcoin, diagnose if bitcoin are a systematic risk asset, and evaluate their effectiveness by estimating market beta representing systematic risk using GARCH (Generalized Auto Regressive Conditional Heteroskedastieity) model. First, the empirical results showed that the market beta of Bitcoin using the OLS model was estimated at 0.7745. Second, using GARCH (1, 2) model, the market beta of Bitcoin was estimated to be significant, and the effects of ARCH and GARCH were found to be significant over time, resulting in conditional volatility. Third, the estimated market beta of the GARCH (1, 2), AR (1)-GARCH (1), and MA (1)-GARCH (1, 2) models were also less than 1 at 0.8819, 0.8835, and 0.8775 respectively, showing that there is no systematic risk. Finally, in terms of efficiency, GARCH model was more efficient because the standard error of a market beta was less than that of the OLS model. Among the GARCH models, the MA (1)-GARCH (1, 2) model considering non-simultaneous transactions was estimated to be the most appropriate model.