• Journal of the Korean Data and Information Science Society
• /
• v.27 no.6
• /
• pp.1661-1671
• /
• 2016

Risk analysis is a systematic study of uncertainties and risks we encounter in business, engineering, public policy, and many other areas. Value at Risk (VaR) is one of the most widely used risk measurements in risk management. In this paper, the Korean Composite Stock Price Index data has been utilized to model the VaR employing the classical ARMA (1,1)-GARCH (1,1) models with normal, t, generalized hyperbolic, and generalized pareto distributed errors. The aim of this paper is to compare the performance of each model in estimating the VaR. The performance of models were compared in terms of the number of VaR violations and Kupiec exceedance test. The GARCH-GPD likelihood ratio unconditional test statistic has been found to have the smallest value among the models.

• Communications for Statistical Applications and Methods
• /
• v.16 no.4
• /
• pp.587-594
• /
• 2009

In this paper the change point problem of the error terms in linear regression models is considered. Since fixed or stochastic independent variables and weakly dependent errors are assumed, usual multiple regression models and time series models including ARMA are covered. We use the estimates of probability density function based on residuals in order to test the distribution change of the unobserved errors. Under some mild conditions, the test using the residuals is proved to have the same limiting distribution as the test based on true errors.

• Journal of the Korean Statistical Society
• /
• v.36 no.2
• /
• pp.183-200
• /
• 2007

We consider a nonlinear autoregressive moving average model with nonlinear GARCH errors, and find sufficient conditions for the existence of a strictly stationary solution of three related time series equations. We also consider a geometric ergodicity and functional central limit theorem for a nonlinear autoregressive model with nonlinear ARCH errors. The given model includes broad classes of nonlinear models. New results are obtained, and known results are shown to emerge as special cases.

• Journal of the Korean Statistical Society
• /
• v.28 no.4
• /
• pp.503-513
• /
• 1999

The Bayes factor for the identification of stationary ARM(p,q) models is exactly computed using the Monte Carlo method. As priors are used the uniform prior for (\ulcorner,\ulcorner) in its stationarity-invertibility region, the Jefferys prior and the reference prior that are noninformative improper for ($\mu$,$\sigma$\ulcorner).

• Smart Structures and Systems
• /
• v.26 no.1
• /
• pp.23-33
• /
• 2020

Majority of the damage in engineering structures is nonlinear. Damage sensitive features (DSFs) extracted by traditional methods from linear time series models cannot effectively handle nonlinearity induced by structural damage. A new DSF is proposed based on vector space cosine similarity (VSCS), which combines K-means cluster analysis and Bayesian discrimination to detect nonlinear structural damage. A reference autoregressive moving average (ARMA) model is built based on measured acceleration data. This study first considers an existing DSF, residual standard deviation (RSD). The DSF is further advanced using the VSCS, and then the advanced VSCS is classified using K-means cluster analysis and Bayes discriminant analysis, respectively. The performance of the proposed approach is then verified using experimental data from a three-story shear building structure, and compared with the results of existing RSD. It is demonstrated that combining the linear ARMA model and the advanced VSCS, with cluster analysis and Bayes discriminant analysis, respectively, is an effective approach for detection of nonlinear damage. This approach improves the reliability and accuracy of the nonlinear damage detection using the linear model and significantly reduces the computational cost. The results indicate that the proposed approach is potential to be a promising damage detection technique.

• Proceedings of the KIEE Conference
• /
• 2015.07a
• /
• pp.329-330
• /
• 2015

From the results of previous my paper [10] in 2015 year of economic and electrical power storage research conference in Naju, this paper describes an application of autoregressive and moving average (ARMA) model to forecast hourly average wind speed (HAWS) in Jeju island. The models are used to build up short-term forecast of hourly average wind speed by the weighted sum of previous wind speed values.

• Journal of Intelligence and Information Systems
• /
• v.1 no.1
• /
• pp.135-148
• /
• 1995

Neural Networks have been advocated as an alternative to statistical forecasting methods. However, the empirical evidences are not consistent. In the present experiments, multi-layered perceptron (MLP) are adopted as approximator to the time series generating processes. To prevent the MLP from being overfitted to the given time series, the information obtained from ARMA modeling is used to determine the architecture of MLP. The proposed approach was tested empirically using the subsamples of the 111 time series used in the first Markridakis Competition. The forecasting results were analyzed to find out the factors that affect the performance of MLP. The experimental results show that the proposed approach outperforms ARMA models in terms of fitting and forecasting accuracy. In addition, it is found that the use of deseasonalized data improves the forecasting accuracy of MLP.

• Journal of applied mathematics & informatics
• /
• v.5 no.2
• /
• pp.373-382
• /
• 1998

Most of the works in Time Series Analysis are based on the Auto Regressive Integrated Moving Average (ARIMA) models presented by Box and Jeckins(1976). If the data exhibits no ap-parent deviation from stationarity and if it has rapidly decreasing autocorrelation function then a suitable ARIMA(p,q) model is fit to the given data. Selection of the orders of p and q is one of the crucial steps in Time Series Analysis. Most of the methods to determine p and q are based on the autocorrelation function and partial autocor-relation function as suggested by Box and Jenkins (1976). many new techniques have emerged in the literature and it is found that most of them are over very little use in determining the orders of p and q when both of them are non-zero. The Durbin-Levinson algorithm and Innovation algorithm (Brockwell and Davis 1987) are used as recur-sive methods for computing best linear predictors in an ARMA(p,q)model. These algorithms are modified to yield an effective method for ARMA model identification so that the values of order p and q can be determined from them. The new method is developed and its validity and usefulness is illustrated by many theoretical examples. This method can also be applied to an real world data.

• Journal of Institute of Control, Robotics and Systems
• /
• v.2 no.4
• /
• pp.344-350
• /
• 1996

An adaptive predictive level control of waste heat steam boiler was studied by using mathematical models considering the inverse response. The simulation experiments of the model identification were performed by using linear and bilinear models. From the results of simulations it was found that the bilinear model represented the actual dynamic behavior of steam boiler very well. ARMA model was used in the model identification and the adaptive predictive controller. To verify the performance and effectiveness of the adaptive predictive controller used in this study the simulation results of the adaptive predictive level control for waste heat steam boiler based on bilinear model were compared to those of P, PI and PID controller. The results of simulations showed that the adaptive predictive controller provides the fast arrival to setpoint of liquid level.

• Journal of Korean Society for Quality Management
• /
• v.36 no.4
• /
• pp.87-92
• /
• 2008

It is common to use CUSUM charts for detecting small level shifts in processes control, in which reference value(k) and decision interval(h) are the design parameters to be determined. To control process with autocorrelation, CUSUM charts could be applied to residuals obtained from fitting ARIMA models. However, constant level shifts in processes lead to varying mean shifts in residual processes and thus standard CUSUM charts may need to be modified. In this paper, we study the performance of CUSUM charts with various design parameters applied to autocorrelated processes, especially focussing on ARMA(1,1) models, and propose how they can be determined to get better performance in terms of the average run length.