• Quantitative Bio-Science
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• v.37 no.2
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• pp.73-79
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• 2018

As high frequency (HF, for short) time series is now prevalent in the presence of real time big data, volatility computations based on traditional ARCH/GARCH models need to be further developed to suit the high frequency characteristics. This article reviews realized volatilities (RV) and multivariate GARCH (MGARCH) to deal with high frequency volatility computations. As a (functional) infinite dimensional models, the fARCH and fGARCH are introduced to accommodate ultra high frequency (UHF) volatilities. The fARCH and fGARCH models are developed in the recent literature by Hormann et al. [1] and Aue et al. [2], respectively, and our discussions are mainly based on these two key articles. Real data applications to domestic UHF financial time series are illustrated.

• The Korean Journal of Applied Statistics
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• v.31 no.5
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• pp.667-675
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• 2018

When a financial time series consists of daily (closing) returns, traditional volatility models such as autoregressive conditional heteroskedasticity (ARCH) and generalized ARCH (GARCH) are useful to figure out daily volatilities. With high frequency returns in a day, one may adopt various multivariate GARCH techniques (MGARCH) (Tsay, Multivariate Time Series Analysis With R and Financial Application, John Wiley, 2014) to obtain intraday volatilities as long as the high frequency is moderate. When it comes to the ultra high frequency (UHF) case (e.g., one minute prices are available everyday), a new model needs to be developed to suit UHF time series in order to figure out continuous time intraday-volatilities. Aue et al. (Journal of Time Series Analysis, 38, 3-21; 2017) proposed functional GARCH (fGARCH) to analyze functional volatilities based on UHF data. This article introduces fGARCH to the readers and illustrates how to estimate fGARCH equations using UHF data of KOSPI and Hyundai motor company.

• The Korean Journal of Applied Statistics
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• v.30 no.6
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• pp.983-991
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• 2017

High frequency time series are now prevalent in financial data. However, models need to be further developed to suit high frequency time series that account for intraday volatilities since traditional volatility models such as ARCH and GARCH are concerned only with daily volatilities. Due to $H{\ddot{o}}rmann$ et al. (2013), functional ARCH abbreviated as fARCH is proposed to analyze intraday volatilities based on high frequency time series. This article introduces fARCH to readers that illustrate intraday volatility configuration on the KOSPI and the Hyundai motor company based on the data with one minute high frequency.

• The Korean Journal of Financial Management
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• v.24 no.3
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• pp.63-89
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• 2007

This study aims at empirically verifying whether long memory properties exist in returns and volatility of the financial time series and then, empirically observing influential factors of long-memory properties. The presence of long memory properties in the financial time series is examined with the Hurst exponent. The Hurst exponent is measured by DFA(detrended fluctuation analysis). The empirical results are summarized as follows. First, the presence of significant long memory properties is not identified in return time series. But, in volatility time series, as the Hurst exponent has the high value on average, a strong presence of long memory properties is observed. Then, according to the results empirically confirming influential factors of long memory properties, as the Hurst exponent measured with volatility of residual returns filtered by GARCH(1, 1) model reflecting properties of volatility clustering has the level of $H{\approx}0.5$ on average, long memory properties presented in the data before filtering are no longer observed. That is, we positively find out that the observed long memory properties are considerably due to volatility clustering effect.