• Journal of the Korean Data and Information Science Society
• /
• v.28 no.3
• /
• pp.697-707
• /
• 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.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.19 no.3
• /
• pp.697-704
• /
• 1995

The dynamic characteristics of a system can be critically influenced by system uncertainty, so the dynamic system must be analyzed stochastically in consideration of system uncertainty. This study presents the stochastic model of a nonlinear dynamic system with uncertain parameters under nonstationary stochastic inputs. And this stochastic system is analyzed by a new stochastic process closure method and moment equation method. The first moment equation is numerically evaluated by Runge-Kutta method and the second moment equation is numerically evaluated by stochastic process closure method, 4th cumulant neglect closure method and Runge-Kutta method. But the first and the second moment equations are coupled each other, so this equations are approximately evaluated by a iterative method. Finally the accuracy of the present method is verified by Monte Carlo simulation.

• Computational Structural Engineering
• /
• v.8 no.3
• /
• pp.113-122
• /
• 1995

The purpose of this study is to evaluate performance and safety of structures designed according to current seismic code or provisions (e.g., Uniform Building Code(UBC), NEHRP provisions, etc.) during lifetime of structures. The performance is represented in terns of reliability in this paper. To perform reliability analyses, a large number of time history response analyses for a given structure are usually required. In this study, to perform reliability analyses ground motions are generated based on nonstationary random process and structures are designed based on UBC. In this paper, responses of structures under a given earthquake is evaluated using dynamic nonlinear time history analyses and also an equivalent nonlinear system (ENS) with response scaling factors. The ENS system is described in the companion paper. Therefore, this paper evaluates the seismic performance of structures and also verify the accuracy of ENS.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1999.04a
• /
• pp.145-150
• /
• 1999

In the nonlinear dynamic structural analysis, the given ground excitation as an input should be well defined. Because of the lack of recorded accelerograms in Korea, it is required to generate an artificial earthquake by a stochastic model of ground excitation with various dynamic properties rather than recorded accelerograms. It is well known that earthquake motions are generally non-stationary with time-varying intensity and frequency content. Many researchers have proposed non-stationary random process models. Yeh and Wen (1990) proposed a non-stationary stochastic process model which can be modeled as components with an intensity function, a frequency modulation function and a power spectral density function to describe such non-stationary characteristics. This paper shows the process to generate nonstationary artificial earthquake ground motions considering target design response spectrum chosen by ATC14.

• Journal of the Korean Society for Precision Engineering
• /
• v.12 no.4
• /
• pp.127-134
• /
• 1995

The dynamic characteristics of a system can be critically influenced by system uncertainty, so the dynamic system must be analyzed stochastically in consideration of system uncertainty. This study presents a generalized stochastic model of dynamic system subjected to bot external and parametric nonstationary stochastic input. And this stochastic system is analyzed by a new stochastic process closure method and moment equation method. The first moment equation is numerically evaluated by Runge-Kutta method. But the second moment equation is founded to constitute an infinite coupled set of differential equations, so this equations are numerically evaluated by cumulant neglect closure method and Runge-Kutta method. Finally the accuracy of the present method is verified by Monte Carlo simulation.

• Management Science and Financial Engineering
• /
• v.17 no.2
• /
• pp.85-97
• /
• 2011

In this study we examine the long term behavior of stock returns. The analysis reveals that negative autocorrelations of the returns exist for a super-long horizon as long as 10 years. This pattern, however, contrasts to predictions of previous stock price models which include random walks. We suggest the introduction of a fractionally integrated process into a nonstationary component of stock prices, and demonstrate empirically the existence of the process in NYSE stock returns. The predicted values of autocorrelation from our stock price model confirm the super-long term behavior of the returns observed in regression, indicating that inefficiency in the stock market could remain for a long time.

• Environmental Engineering Research
• /
• v.10 no.2
• /
• pp.88-103
• /
• 2005

In this paper, data-driven modeling and multiresolution analysis (MRA) are applied for a full-scale wastewater treatment plant (WWTP). The proposed method is based on modeling by partial least squares (PLS) and multiscale monitoring by a generic dissimilarity measure (GDM), which is suitable for nonstationary and non-normal process monitoring such as a biological process. Case study in an industrial plant showed that the PLS model could give good modeling performance and analyze the dynamics of a complex plant and MRA was useful to detect and isolate various faults due to its multiscale nature. The proposed method enables us to show the underlying phenomena as well as to filter out unwanted and disturbing phenomena.

• Communications for Statistical Applications and Methods
• /
• v.26 no.1
• /
• pp.27-34
• /
• 2019

We study the effect of detrending on the coherency between two time series processes. Many economic and financial time series variables include nonstationary components; however, we analyze the two most popular cases of stochastic and deterministic trends. We analyze the asymptotic behavior of coherency under incorrect detrending, which includes the cases of first-differencing the deterministic trend process and, conversely, the time trend removal of the unit root process. A simulation study is performed to investigate the finite sample performance of the sample coherency due to incorrect detrending. Our work is expected to draw attention to the possible distortion of coherency when the series are incorrectly detrended. Further, our results can extend to various specification of trends in aggregate time series variables.

• Structural Engineering and Mechanics
• /
• v.47 no.3
• /
• pp.361-381
• /
• 2013

A Bayesian probabilistic method is proposed for online estimation of the process noise and measurement noise parameters for Kalman filter. Kalman filter is a well-known recursive algorithm for state estimation of dynamical systems. In this algorithm, it is required to prescribe the covariance matrices of the process noise and measurement noise. However, inappropriate choice of these covariance matrices substantially deteriorates the performance of the Kalman filter. In this paper, a probabilistic method is proposed for online estimation of the noise parameters which govern the noise covariance matrices. The proposed Bayesian method not only estimates the optimal noise parameters but also quantifies the associated estimation uncertainty in an online manner. By utilizing the estimated noise parameters, reliable state estimation can be accomplished. Moreover, the proposed method does not assume any stationarity condition of the process noise and/or measurement noise. By removing the stationarity constraint, the proposed method enhances the applicability of the state estimation algorithm for nonstationary circumstances generally encountered in practice. To illustrate the efficacy and efficiency of the proposed method, examples using a fifty-story building with different stationarity scenarios of the process noise and measurement noise are presented.

• Current Optics and Photonics
• /
• v.5 no.3
• /
• pp.322-328
• /
• 2021

In this paper, a pretreatment method for a matrix in convex optimization is proposed to optimize the spectral reconstruction process of a disordered dispersion spectrometer. Unlike the reconstruction process of traditional spectrometers using Fourier transforms, the reconstruction process of disordered dispersion spectrometers involves solving a large-scale matrix equation. However, since the matrices in the matrix equation are obtained through measurement, they contain uncertainties due to out of band signals, background noise, rounding errors, temperature variations and so on. It is difficult to solve such a matrix equation by using ordinary nonstationary iterative methods, owing to instability problems. Although the smoothing Tikhonov regularization approach has the ability to approximatively solve the matrix equation and reconstruct most simple spectral shapes, it still suffers the limitations of reconstructing complex and irregular spectral shapes that are commonly used to distinguish different elements of detected targets with mixed substances by characteristic spectral peaks. Therefore, we propose a special pretreatment method for a matrix in convex optimization, which has been proved to be useful for reducing the condition number of matrices in the equation. In comparison with the reconstructed spectra gotten by the previous ordinary iterative method, the spectra obtained by the pretreatment method show obvious accuracy.