• Journal of the Korean Data and Information Science Society
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• v.18 no.1
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• pp.211-218
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• 2007

Nonlinear ARMA model $X_n\;=\;h(X_{n-1},{\cdots},X_{n-p},e_{n-1},{\cdots},e_{n-p})+e_n$ is considered and easy-to-check sufficient condition for strict stationarity of {$X_n$} without some irreducibility or continuity assumption is given. Threshold ARMA(p, q) and momentum threshold ARMA(p, q) models are examined as special cases.

• Journal of the Korean Statistical Society
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• v.36 no.2
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• pp.183-200
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• 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 Data and Information Science Society
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• v.18 no.1
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• pp.237-245
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• 2007

Nonlinear asymmetric time series models have the growing interest in econometrics and finance. Threshold model is one of the successful asymmetric model. We consider a smooth transition ARMA model which converges a.s. to a threshold ARMA model and show that the smooth transition ARMA model admits a stationary measure, provided a suitable condition on the coefficients of the autoregressive parts of the different regimes is satisfied. Stationarity of a smooth transition GARCH model is also obtained.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.754-759
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• 1993

An adaptive model predictive control (AMPC) strategy using auto-regression moving-average (ARMA) models is presented. The characteristic features of this methodology are the small computer memory requirement, high computational speed, robustness, and easy handling of nonlinear and time varying MIMO systems. Since the process dynamic behaviors are expressed by ARMA models, the model parameter adaptation is simple and fast to converge. The recursive least square (RLS) method with exponential forgetting is used to trace the process model parameters assuming the process is slowly time varying. The control performance of the AMPC is verified by both comparative simulation and experimental studies on distillation column control.

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

• 제어로봇시스템학회:학술대회논문집
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• 1999.10a
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• pp.45-48
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• 1999

Model predictive control algorithm requires a relevant model of the system to be controlled. Unfortunately, the first principle model describing a polymerization reaction system has a large number of parameters to be estimated. Thus there is a need for the identification and control of a polymerization reactor system by using available input-output data. In this work, the polynomial auto-regressive moving average (ARMA) models are employed as the input-output model and combined into the nonlinear model predictive control algorithm based on the successive linearization method. Simulations are conducted to identify the continuous styrene polymerization reactor system. The input variables are the jacket inlet temperature and the feed flow rate whereas the output variables are the monomer conversion and the weight-average molecular weight. The polynomial ARMA models obtained by the system identification are used to control the monomer conversion and the weight-average molecular weight in a continuous styrene polymerization reactor It is demonstrated that the nonlinear model predictive controller based on the polynomial ARMA model tracks the step changes in the setpoint satisfactorily. In conclusion, the polynomial ARMA model is proven effective in controlling the continuous styrene polymerization reactor.

• Proceedings of the Korean Statistical Society Conference
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• 2000.11a
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• pp.267-269
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• 2000

Using the fuzzified coefficients, ARMA processes can be extended to fuzzy time series model. In this paper, the estimation of parameters in the fuzzy time series model with asymmetric triangular fuzzy coefficients is studied. Nonlinear programming is applied to get solutions of parameters.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.35S no.10
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• pp.166-174
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• 1998

Neural networks, having highly nonlinear dynamics by virtue of the distributed nonlinearities and the learing ability, have the potential for the adaptive prediction of nonstationary signals. This paper describes the nonlinear prediction of these signals in two ways; using a nonlinear module and the cascade combination of nonlinear and linear modules. Fully-connected recurrent neural networks (RNNs) and a conventional tapped-delay-line (TDL) filter are used as the nonlinear and linear modules respectively. The dynamic behavior of the proposed predictors is demonstrated for chaotic time series adn speech signals. For the relative comparison of prediction performance, the proposed predictors are compared with a conventional ARMA linear prediction model. Experimental results show that the neural networks based adaptive predictor ourperforms the traditional linear scheme significantly. We also find that the cascade combination predictor is well suitable for the prediction of the time series which contain large variations of signal amplitude.

• Journal of the Korean Data and Information Science Society
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• v.15 no.4
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• pp.783-791
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• 2004

In this paper we review recent developments in nonlinear time series modeling on both conditional mean and conditional variance. Traditional linear model in conditional mean is referred to as ARMA(autoregressive moving average) process investigated by Box and Jenkins(1976). Nonlinear mean models such as threshold, exponential and random coefficient models are reviewed and their characteristics are explained. In terms of conditional variances, ARCH(autoregressive conditional heteroscedasticity) class is considered as typical linear models. As nonlinear variants of ARCH, diverse nonlinear models appearing in recent literature including threshold ARCH, beta-ARCH and Box-Cox ARCH models are remarked. Also, a class of unified nonlinear models are considered and parameter estimation for that class is briefly discussed.

• Journal of Korea Water Resources Association
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• v.54 no.spc1
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• pp.1083-1093
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• 2021

It is an essential to predict water usage for establishing an optimal supply operation plan and reducing power consumption. However, the water usage by consumer has a non-linear characteristics due to various factors such as user type, usage pattern, and weather condition. Therefore, in order to predict the water consumption, we proposed the methodology linking various techniques that can consider non-linear characteristics of water use and we called it as KWD framework. Say, K-means (K) cluster analysis was performed to classify similar patterns according to usage of each individual consumer; then Wavelet (W) transform was applied to derive main periodic pattern of the usage by removing noise components; also, Deep (D) learning algorithm was used for trying to do learning of non-linear characteristics of water usage. The performance of a proposed framework or model was analyzed by comparing with the ARMA model, which is a linear time series model. As a result, the proposed model showed the correlation of 92% and ARMA model showed about 39%. Therefore, we had known that the performance of the proposed model was better than a linear time series model and KWD framework could be used for other nonlinear time series which has similar pattern with water usage. Therefore, if the KWD framework is used, it will be possible to accurately predict water usage and establish an optimal supply plan every the various event.