• Journal of the Korean Data and Information Science Society
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• 제28권3호
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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.

• 응용통계연구
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• 제23권4호
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• pp.683-692
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• 2010

본 논문에서는 연속형-GARCH 시계열 자료인 금융 시계열 자료에 대해서 클리핑(clipping)을 통해 얻은 이항(binary) 범주형 시계열을 분석하고 응용하는 방안에 대해 연구하고 있다. 모수추정 방법을 소개하고 있으며 이를 이용하여 이분산 시계열과 연관된 확률을 추정하는 방법을 예시하였다.

• 대한수학회논문집
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• 제18권3호
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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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• 제21권4호
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• pp.327-334
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• 2014

Various modified GARCH(1, 1) models have been found adequate in many applications. We are interested in their continuous time versions and limiting properties. We first define a stochastic integral that includes useful continuous time versions of modified GARCH(1, 1) processes and give sufficient conditions under which the process is exponentially ergodic and ${\beta}$-mixing. The central limit theorem for the process is also obtained.

• Communications for Statistical Applications and Methods
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• 제14권1호
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• pp.141-146
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• 2007

In this paper, we consider a Box-Cox transformed threshold GARCH(1,1) process and find a sufficient condition under which the process is geometrically ergodic and has the ${\beta}$-mixing property with an exponential decay rate.

• Journal of the Korean Data and Information Science Society
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• 제21권6호
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• pp.1311-1317
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• 2010

A continuous time asymmetric power GARCH(1,1) model is suggested, based on a single background driving L$\'{e}$vy process. The stochastic differential equation for the given process is derived and the strict stationarity and kth order moment conditions are examined.

• Communications for Statistical Applications and Methods
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• 제19권5호
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• pp.639-646
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• 2012

The exponential continuous time GARCH(p,q) model for financial assets suggested by Haug and Czado (2007) is considered, where the log volatility process is driven by a general L$\acute{e}$vy process and the price process is then obtained by using the same L$\acute{e}$vy process as driving noise. Uniform ergodicity and ${\beta}$-mixing property of the log volatility process is obtained by adopting an extended generator and drift condition.

• Journal of the Korean Data and Information Science Society
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• 제22권2호
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• pp.353-360
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• 2011

We consider an asymmetric power transformed threshold GARCH(1.1) process and find sufficient conditions for the existence of a strictly stationary solution, geometric ergodicity and ${\beta}$-mixing property. Moments conditions are given. Box-Cox transformed threshold GARCH(1.1) is also considered as a special case.

• 응용통계연구
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• 제24권1호
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• pp.61-69
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• 2011

다양한 GARCH류 모형들의 변동성 함수를 살펴보면 흥미롭게도 거의 대부분 모형에서 수익률의 일차항( rst or der term)이나 수익률과 변동성의 교차항(interaction term)이 나타나지 않는다. 일차항과 교차항은 변동성의 비대칭성을 설명하는 역할을 할 수 있으며 $h_t$의 회귀분석식의 형태로 볼 때 변동성 함수의 일반적인 이차형식(quadratic form)을 구성한다고 할 수 있다. 본 논문에서는 변동성과 수익률들 사이의 교차항 및 일차항을 포함한 이차형식(quadratic form) 변동성 모형들을 소개하고, 국내 금융시계열 자료에 적용한 후 비교 분석하고자 한다.

• Communications for Statistical Applications and Methods
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• 제12권3호
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• pp.557-587
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• 2005

This paper elucidates the limiting Gaussian distribution of a class of rank order statistics {$T_N$} for two sample problem pertaining to empirical processes of the squared residuals from two independent samples of GARCH processes. A distinctive feature is that, unlike the residuals of ARMA processes, the asymptotics of {$T_N$} depend on those of GARCH volatility estimators. Based on the asymptotics of {$T_N$}, we empirically assess the relative asymptotic efficiency and effect of the GARCH specification for some GARCH residual distributions. In contrast with the independent, identically distributed or ARMA settings, these studies illuminate some interesting features of GARCH residuals.