• Journal of the Korean Statistical Society
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• 제35권4호
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• pp.453-458
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• 2006

It is well known fact for the iid data that the limiting standard errors of sample autocorrelations are all unity for all time lags and they are asymptotically independent for different lags (Brockwell and Davis, 1991). It is also usual practice in time series modeling that this fact continues to be valid for white noise series which is a sequence of uncorrelated random variables. This paper contradicts this usual practice for white noise. We consider a sequence of martingale differences which belongs to white noise time series and derive exact joint asymptotic distributions of sample autocorrelations. Some implications of the result are illustrated for conditionally heteroscedastic time series.

• Journal of the Korean Statistical Society
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• 제34권2호
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• pp.161-172
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• 2005

In this paper a nonparametric method is proposed for detecting conditionally heteroscedastic errors in a nonparametric time series regression model where the observation points are equally spaced on [0,1]. It turns out that the first-order sample autocorrelation of the squared residuals from the kernel regression estimates provides essential information. Illustrative simulation study is presented for diverse errors such as ARCH(1), GARCH(1,1) and threshold-ARCH(1) models.

• 응용통계연구
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• 제20권1호
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• pp.53-60
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• 2007

시계열 자료 분석에서 ARCH류와 같은 조건부 이분산성 모형을 가정하고 분석하는 모형들이 많이 쓰이고 있다. 실제 우리나라 금융 시계열 자료들을 분석해 보면 비정상성을 나타내는 경우가 드물지 않게 나타난다. 즉, 단위근 형태의 비정상 패턴(integrated phenomenon)에 가까운 경우가 자주 나타난다. 본 논문에서는 다양한 국내 금융시계열 15개에(주가지수, 선물지수, 환율, 이자율 등) GARCH(1,1) 모형을 적합시켜 분산의 지속성을 확인하고, 각 데이터에 첨도(Kurtosis)와 적합된 IGARCH(1,1) 모형을 제시하고자 한다.

• Communications for Statistical Applications and Methods
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• 제17권2호
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• pp.255-261
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• 2010

A class of threshold-asymmetric GRACH(TGARCH, hereafter) models has been useful for explaining asymmetric volatilities in the field of financial time series. The cumulative impulse response function of a conditionally heteroscedastic time series often measures a degree of unstability in volatilities. In this article, a general form of the cumulative impulse response function of the TGARCH model is discussed. In particular, We present formula in their closed forms for the first two lower order models, viz., TGARCH(1, 1) and TGARCH(2, 2).