• Quantitative Bio-Science
• /
• v.37 no.2
• /
• pp.73-79
• /
• 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
• /
• v.33 no.6
• /
• pp.805-812
• /
• 2020

High-frequency data are now prevalent in financial time series. As a functional data arising from high-frequency financial time series, we are concerned with the intraday volatility to which functional principal component analysis (FPCA) is applied in order to achieve a dimension reduction. A review on FPCA and R function is made and high-frequency KOSPI volatility is analysed as an application.

• The Korean Journal of Applied Statistics
• /
• v.30 no.6
• /
• pp.983-991
• /
• 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 Applied Statistics
• /
• v.31 no.5
• /
• pp.667-675
• /
• 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
• /
• v.33 no.3
• /
• pp.297-308
• /
• 2020

We focus on the functional autoregressive conditional heteroscedasticity (fARCH) modelling to analyze intraday volatilities based on high frequency financial time series. Multivariate volatility models are investigated to approximate fARCH(1). A formula of multi-step ahead volatilities for fARCH(1) model is derived. As an application, in implementing fARCH(1), a choice of appropriate time interval for the intraday return is discussed. High frequency KOSPI data analysis is conducted to illustrate the main contributions of the article.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.14 no.4
• /
• pp.249-273
• /
• 2010

Often in practice, the implied volatility of an option is calculated to find the option price tomorrow or the prices of, nearby' options. To show that one does not need to adhere to the Black- Scholes formula in this scheme, Figlewski has provided a new pricing formula and has shown that his, alternating passive model' performs as well as the Black-Scholes formula [8]. The Figlewski model was modified by Henderson et al. so that the formula would have no static arbitrage [10]. In this paper, we show how to construct a huge class of such static no arbitrage pricing functions, making use of distortions, coherent risk measures and the pricing theory in incomplete markets by Carr et al. [4]. Through this construction, we provide a more elaborate static no arbitrage pricing formula than Black-Sholes in the above scheme. Moreover, using our pricing formula, we find a volatility curve which fits with striking accuracy the synthetic data used by Henderson et al. [10].

• Communications for Statistical Applications and Methods
• /
• v.31 no.1
• /
• pp.87-104
• /
• 2024

Most functional magnetic resonance imaging (fMRI) studies in resting state have assumed that the functional connectivity (FC) between time series from distinct brain regions is constant. However, increased interest has recently been in quantifying possible dynamic changes in FC during fMRI experiments. FC study may provide insight into the fundamental workings of brain networks to brain activity. In this work, we focus on the specific problem of estimating the dynamic behavior of pairwise correlations between time courses extracted from two different brain regions. We compare the sliding-window techniques such as moving average (MA) and exponentially weighted moving average (EWMA), dynamic causality with vector autoregressive (VAR) model, dynamic conditional correlation (DCC) based on volatility, and the proposed alternative methods to use differencing and recursive residuals. We investigate the properties of those techniques in a series of simulation studies. We also provide an application with major depressive disorder (MDD) patient fMRI data to demonstrate studying dynamic correlations.

• The Korean Journal of Applied Statistics
• /
• v.32 no.1
• /
• pp.69-81
• /
• 2019

We consider bivariate long range dependent (LRD) time series forecasting using a deep learning method. A long short-term memory (LSTM) network well-suited to time series data is applied to forecast bivariate time series; in addition, we compare the forecasting performance with bivariate fractional autoregressive integrated moving average (FARIMA) models. Out-of-sample forecasting errors are compared with various performance measures for functional MRI (fMRI) data and daily realized volatility data. The results show a subtle difference in the predicted values of the FIVARMA model and VARFIMA model. LSTM is computationally demanding due to hyper-parameter selection, but is more stable and the forecasting performance is competitively good to that of parametric long range dependent time series models.

• Elastomers and Composites
• /
• v.29 no.3
• /
• pp.226-233
• /
• 1994

The properties of the mixed prepolymer-urethane in the range of 10-40 phr were observed. LBR and LCR have same functional group but different in structure of molecular. The viscosity of mixture depending on content of rubber, adhesive strength, thermal property and compatibility with a diluted solvent are as follows: 1. The viscosity of the mixture was influenced by solubility of the diluent for urethane resin and liquid rubber. 2. Adhesive strength showed the highest value at 30phr rubber, decreased gradually at above 30phr rubber. And LBR revealed better physical property than that of LCR. 3. The most effective factors affecting adhesive strength are molecular structure of rubber, the type of solvent, and volatility. 4. Urethane resin containing LBR showed better compatibility for solvent and faster drying velocity. 5. LBR showed more favorable compatibility and dispersion state than those of LCR by analyzing the results of SEM.

• The Korean Journal of Applied Statistics
• /
• v.27 no.6
• /
• pp.959-973
• /
• 2014

Asset pricing models that account for asymmetric volatility in asset prices have been recently proposed. This article presents an efficient Bayesian method to analyze asset-pricing models. The method is developed by devising a partially collapsed Gibbs sampler that capitalizes on the functional incompatibility of conditional distributions without complicating the updates of model components. The proposed method is illustrated using simulated data and applied to daily S&P 500 data observed from September 1980 to August 2014.