• Proceedings of the Korea Water Resources Association Conference
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• 2005.05b
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• pp.792-796
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• 2005

The methods of times series analysis have been recognized as important tools for assisting in solving problems related to the management of water resources. Especially, After more than 40 years the so-called Hurst effect remains an open problem in stochastic hydrology. Until now, its existence has been explained fly R/S analysis that roots in early work of the British hydrologist H.E. Hurst(1951). Today, the Hurst analysis is mostly used for the hydrological studies for memory and characteristics of time series and many methodologies have been developed for the analysis. So, there are many different techniques for the estimation of the Hurst exponent(H). However, the techniques can produce different characteristics for the persistence of a time series each other. We found that DFA is the most appropriate technique for the Hurst exponent estimation for both the shot term memory and long term memory. We analyze the SOI(Southern Oscillations Index) and 6 tree-ring series for USA sites by means of DFA and the BDS statistic is used for nonlinearity test of the series. From the results, we found that SOI series is nonlinear time series which has a long term memory of H=0.92. Contrary to earlier work of Rao(1999), all the tree- ring series are not random from our analysis. A certain tree ring series show a long term memory of H=0.97 and nonlinear property. Therefore, we can say that the SOI and tree-ring series may show long memory and nonlinearity.

• Communications for Statistical Applications and Methods
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• v.22 no.3
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• pp.295-304
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• 2015

This paper considers the problem of estimation of the Hurst parameter H ${\in}$ (1/2, 1) from longitudinal data with the error term of a fractional Brownian motion with Hurst parameter H that gives the amount of the long memory of its increment. We provide a new estimator of Hurst parameter H using a two scale sampling method based on $A{\ddot{i}}t$-Sahalia and Jacod (2009). Asymptotic behaviors (consistent and central limit theorem) of the proposed estimator will be investigated. For the proof of a central limit theorem, we use recent results on necessary and sufficient conditions for multi-dimensional vectors of multiple stochastic integrals to converges in distribution to multivariate normal distribution studied by Nourdin et al. (2010), Nualart and Ortiz-Latorre (2008), and Peccati and Tudor (2005).

• 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.

• Communications for Statistical Applications and Methods
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• v.24 no.5
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• pp.481-492
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• 2017

This paper investigates a convergence rate of a test statistics given by two scale sampling method based on $A\ddot{i}t$-Sahalia and Jacod (Annals of Statistics, 37, 184-222, 2009). This statistics tests for longitudinal data having the existence of long memory dependence driven by fractional Brownian motion with Hurst parameter $H{\in}(1/2,\;1)$. We obtain an upper bound in the Kolmogorov distance for normal approximation of this test statistic. As a main tool for our works, the recent results in Nourdin and Peccati (Probability Theory and Related Fields, 145, 75-118, 2009; Annals of Probability, 37, 2231-2261, 2009) will be used. These results are obtained by employing techniques based on the combination between Malliavin calculus and Stein's method for normal approximation.

• Journal of Korea Water Resources Association
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• v.37 no.12
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• pp.993-1007
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• 2004

There are many different techniques for the estimation of the Hurst exponent. However, the techniques can produce different characteristics for the persistence of a time series each other. This study uses several techniques such as adjusted range, resealed range(RR) analysis, modified restated range(MRR) analysis, 1/f power spectral density analysis, Maximum Likelihood Estimation(MLE), detrended fluctuations analysis(DFA), and aggregated variance time(AVT)method for the Hurst exponent estimation. The generated time series from chaos and stochastic systems are analyzed for the comparative study of the techniques. Then this study discusses the advantages and disadvantages of the techniques and also the limitations of them.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1998.10a
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• pp.271-274
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• 1998

In this paper we examine long-term memory of the financial time-series by employing the R/S analysis, the Hurst exponent estimation, and the modified R/S analysis. The null hypothesis of white-noise is tested using the NYSE daily indexes from January 1966 to July 1998, and the results show that long-range dependence exists before the apparent structural break of the Black Monday in 1987.

• Journal of Information Technology Applications and Management
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• v.21 no.3
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• pp.1-17
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• 2014

In this study, various characteristics of R&D related economic variables were studied to analyze complexity of science and technology activities in Korea, as reliance of R&D activities of the private sector is growing by the day. In comparison to other countries, this means that it is likely to be fluctuated by economic conditions. This complexity characteristic signifies that the result of science and technology activities can be greatly different from the anticipated results - depending on the influences from economic conditions and the results of science and technology activities which may be unpredictable. After reviewing the results of 17 variables related to science and technology characteristics of complex systems intended for time-series data - in the total R&D expenditure, and private R&D expenditure, numbers of SCI papers, the existence of chaotic characteristics were. using Lyapunov Exponent, Hurst Exponent, BDS test. This result reveals science and technology activity of the three most important components in Korea which are; heavy dependence on initial condition, the long term memory of time series, and non-linear structure. As stable R&D investment and result are needed in order to maintain steady development of Korea economy, the R&D structure should be less influenced by business cycles and more effective technology development policy for improving human resource development must be set in motion. And to minimize the risk of new technology, the construction of sophisticated technology forecasting system should take into account, for development of R&D system.

• The Bulletin of The Korean Astronomical Society
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• v.36 no.1
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• pp.40.1-40.1
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• 2011

Large solar flares are associated with various aspects of space weather effects. Numerous attempts have been made to predict when the solar flare will be occurred mainly based on the configuration of the magnetic field of its flaring site. We analyze the time series of f/g which indicates a representative measure of the sunspot complexity to see whether it shows a possibility to be predicted without huge amounts of observation. Two kinds of analysis results are presented. One is from its power spectrum giving that there's no significantly persistent periodicity within a few days. Its de-trended fluctuation shows the Hurst exponent larger than 0.5 implying that the f/g time series has a long-term memory in time scales less than 10 days.