• Journal of the Korean Statistical Society
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• v.24 no.1
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• pp.149-160
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• 1995

We consider the problem of optimal adaptive estiamtion of the euclidean parameter vector $\theta$ of the univariate non-linerar autogressive time series model ${X_t}$ which is defined by the following system of stochastic difference equations ; $X_t = \sum^p_{i=1} \theta_i \cdot T_i(X_{t-1})+e_t, t=1, \cdots, n$, where $\theta$ is the unknown parameter vector which descrives the deterministic dynamics of the stochastic process ${X_t}$ and ${e_t}$ is the sequence of white noises with unknown density $f(\cdot)$. Under some general growth conditions on $T_i(\cdot)$ which guarantee ergodicity of the process, we construct a sequence of adaptive estimatros which is locally asymptotic minimax (LAM) efficient and also attains the least possible covariance matrix among all regular estimators for arbitrary symmetric density.

• ETRI Journal
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• v.27 no.2
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• pp.195-205
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• 2005

In this paper, an error-free Butcher algorithm is introduced to study the singular system of a linear electrical circuit for time invariant and time varying cases. The discrete solutions obtained using Runge-Kutta (RK)-Butcher algorithms are compared with the exact solutions of the electrical circuit problem and are found to be very accurate. Stability regions for the single term Walsh series (STWS) method and the RK-Butcher algorithm are presented. Error graphs for inductor currents and capacitor voltages are presented in a graphical form to show the efficiency of the RK-Butcher algorithm. This RK-Butcher algorithm can be easily implemented in a digital computer for any singular system of electrical circuits.

• Journal of Environmental Science International
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• v.22 no.3
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• pp.303-308
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• 2013

This paper proposed a new method for estimating missing values in time series rainfall data. The proposed method integrated the two most widely used estimation methods, general linear model(GLM) and ordinary kriging(OK), by taking a weighted average of covariance matrices derived from each of the two methods. The proposed method was cross-validated using daily rainfall data at thirteen rain gauges in the Hyeong-san River basin. The goodness-of-fit of the proposed method was higher than those of GLM and OK, which can be attributed to the weighting algorithm that was designed to minimize errors caused by violations of assumptions of the two existing methods. This result suggests that the proposed method is more accurate in missing values in time series rainfall data, especially in a region where the assumptions of existing methods are not met, i.e., rainfall varies by season and topography is heterogeneous.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.04a
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• pp.523-527
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• 2004

This paper presents a new design methods of the short-term load forecasting system (STLFS) using the data mining. The proposed predictor takes form of the convex combination of the linear time series predictors for each inputs. The problem of estimating the consequent parameters is formulated by the convex optimization problem, which is to minimize the norm distance between the real load and the output of the linear time series estimator, The problem of estimating the premise parameters is to find the parameter value minimizing the error between the real load and the overall output. Finally, to show the feasibility of the proposed method, this paper provides the short-term load forecasting example.

• 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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.10 no.1
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• pp.31-37
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• 1985

An interesting area of application which makes use of the unique features of the walsh series is that on non-linear stochastic problems. In particular, some success has been obtained in improving the efficiency of signal detection for those transducers which are essentially non-linear in operation. The set of harmonically-related nonorthogonal triangle waves is shown to form a basis apanning the same function space representable by fourier(trigonometric) series. A method for generating nonorthogonal bases for signal representation is presented tailor-made basis function can be used for specific purposes. Fundamental proofs of the basis properties of the representation are examined along with examples illustrating the techniques and computer simulation.

• Journal of KSNVE
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• v.4 no.2
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• pp.137-146
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• 1994

An analytical method for linear free vibration of fully liquid-filled circular cylindrical shell with various boundary conditions is developed by the Fourier series expansion based on the Stokes' transformation. A set of modal displacement functions and their derivatives of a circular cylindrical shell is substituted into the Sanders' shell equations in order to explicitily represent the Fourier coefficients as functions of the end point displacements, forces, and moments. For the vibration relevant to the liquid motion, the velocity potential of liquid is assumed as a sum of linear combination of suitable harmonic functions in the axial directions. The unknown parameter of the velocity potential is selected to satisfy the boundary condition along the wetted shell surface. An explicit expression of the natural frequency equation can be obtained for any kind of classical boundary conditions. The natural frequencies of the liquid-filled cylindrical shells with the clamped-free, the clamped-clamped, and the simply supported-simply supported boundary conditions examined in the previous works, are obtained by the analytical method. The results are compared with the previous works, and excellent agreement is found for the natural frequencies of the shells.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.671-697
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• 2024

In this paper, we formally introduce the notion of a general parametric digamma function Ψ(−s; A, a) and we find the Laurent expansion of Ψ(−s; A, a) at the integers and poles. Considering the contour integrations involving Ψ(−s; A, a), we present some new identities for infinite series involving Dirichlet type parametric harmonic numbers by using the method of residue computation. Then applying these formulas obtained, we establish some explicit relations of parametric linear Euler sums and some special functions (e.g. trigonometric functions, digamma functions, Hurwitz zeta functions etc.). Moreover, some illustrative special cases as well as immediate consequences of the main results are also considered.

• Journal of Digital Convergence
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• v.12 no.7
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• pp.261-266
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• 2014

When the number of parameters in the time series model are diverse, it is hard to forecast because of the increasing error by a parameter estimation. If the homogeneity hypothesis which was obtained from the same model about severeal data for the time series is selected, it is easy to get the predictive value better. Nonlinear time-series panel data for each parameter for each time series, since there are so many parameters that are present, and the large number of parameters according to the parameter estimation error increases the accuracy of the forecast deteriorated. Panel present in the time series of multiple independent homogeneity is satisfied by a comprehensive time series to estimate and to test of the parameters. For studying about the homogeneity test for the m independent non-linear of the time series panel data, it needs to set the model and to make the normal conditions for the model, and to derive the homogeneity test statistic. Finally, it shows to obtain the limit distribution according to ${\chi}^2$ distribution. In actual analysis,, we can examine the result for the homogeneity test about nonlinear time series panel data which are 2 groups of stock price data.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.11a
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• pp.95-98
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• 2005

This paper presents intelligent digital redesign method of global approach for hybrid state space fuzzy-model-based controllers. For effectiveness and stabilization of continuous-time uncertain nonlinear systems under discrete-time controller, Takagi-Sugeno(TS) fuzzy model is used to represent the complex system. And global approach design problems viewed as a convex optimization problem that we minimize the error of the norm bounds between nonlinearly interpolated linear operators to be matched. Also by using the power series, we analyzed nonlinear system's uncertain parts more precisely. When a sampling period is sufficiently small, the conversion of a continuous-time structured uncertain nonlinear system to an equivalent discrete -time system have proper reason. Sufficiently conditions for the global state -matching of the digitally controlled system are formulated in terms of linear matrix inequalities (LMls). Finally, we prove the effectiveness and stabilization of the proposed intelligent digital redesign method by applying the chaotic Lorentz system.