• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.227-234
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• 1996

Consider nonlinear autoregressive processes of order 1 defined by the random iteration $$ (1) X_{n + 1} = f(X_n) + \epsilon_{n + 1} (n \geq 0) $$ where f is real-valued Borel measurable functin on $R^1, {\epsilon_n : n \geq 1}$ is an i.i.d.sequence whose common distribution F has a non-zero absolutely continuous component with a positive density, $E$\mid$\epsilon_n$\mid$ < \infty$, and the initial $X_0$ is independent of ${\epsilon_n : n > \geq 1}$.

• Journal of the Korean Statistical Society
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• v.26 no.4
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• pp.531-541
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• 1997

The asymptotic distribution of residual autocorrelation functions from a generalized p-order random coefficient autoregressive process (GRCA(p)) is derived. To this end, we first describe the GRCA(p) models and then consider the normalised residuals after fitting the model. This result can be applied to the residual analysis for the diagonostic purpose.

• Journal of the Korean Statistical Society
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• v.27 no.2
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• pp.189-195
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• 1998

In this paper, we are concerned with the problem of testing the randomness of the coefficients in a first order autoregressive model. A consistent test based on prediction error is suggested. It is shown that under the null hypothesis, the test statistic is asymptotically normal.

• Journal of the Korean Statistical Society
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• v.31 no.3
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• pp.301-314
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• 2002

For autoregressive moving average (ARMA) models, robust unit root tests are developed using M-estimators. The tests are parametric in the sense ARMA parameters are estimated jointly with unit roots. A Monte-Carlo experiment reveals superiority of the parametric tests over the semipararmetric tests of Lucas (1995a) in terms of both empirical sizes and powers.

• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.959-968
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• 1999

In this paper we are obtained new results for bivariate pro-cesses which help us to tell the dependent structure among hitting times of the processes. We are proposed both dependence properties and the-oretical results among the processes and certain kinds of dependence properties when we are imposed on processes are reflected as analo-gous properties of corresponding hitting times. Finlly we are given some examples to illustrate these concepts.

• Journal of the Korean Operations Research and Management Science Society
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• v.34 no.4
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• pp.91-112
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• 2009

The bullwhip effect means the phenomenon of increasing demand variation as moving UP to the upstream in the supply chain. Therefore, it is recognized that the bullwhip effect is problematic for effective supply chain operations. In this paper, we exactly quantifies the bullwhip effect for the case of stochastic lead time and seasonal demand in two-echelon supply chain where retailer employs a base-stock policy considering SARMA demand processes and stochastic lead time. We also investigate the behavior of the proposed measurement for the bullwhip effect with autoregressive and moving average coefficient, stochastic lead time, and seasonal factor.

• Journal of the Korean Statistical Society
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• v.35 no.1
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• pp.37-47
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• 2006

Recently, as a result of the growing interest in modeling stationary processes with discrete marginal distributions, several models for integer valued time series have been proposed in the literature. One of these models is the integer-valued autoregressive (INAR) models. However, when modeling with integer-valued autoregressive processes, the distributional properties of forecasts have been not yet discovered due to the difficulty in handling the Steutal Van Ham thinning operator 'o' (Steutal and van Ham, 1979). In this study, we derive the mean squared error of h-step-ahead prediction from a Poisson INAR(1) process, reflecting the effect of the variability of parameter estimates in the prediction mean squared error.

• Proceedings of the Korean Statistical Society Conference
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• 2005.11a
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• pp.159-165
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• 2005

Recently, as a result of the growing interest in modelling stationary processes with discrete marginal distributions, several models for integer valued time series have been proposed in the literature. One of theses models is the integer-valued autoregressive(INAR) models. However, when modelling with integer-valued autoregressive processes, there is not yet distributional properties of forecasts, since INAR process contain an accrued level of complexity in using the Steutal and Van Harn(1979) thinning operator 'o'. In this study, a manageable expression for the asymptotic mean square error of predicting more than one-step ahead from an estimated poisson INAR(1) model is derived. And, we present a bootstrap methods developed for the calculation of forecast interval limits of INAR(p) model. Extensive finite sample Monte Carlo experiments are carried out to compare the performance of the several bootstrap procedures.

• Proceedings of the Korea Water Resources Association Conference
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• 2007.05a
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• pp.1437-1440
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• 2007

Many hydroclimatic time series are marked by interannual and longer quasi-period features that are associated with narrow band oscillatory climate modes. A time series modeling approach that directly considers such structures is developed and presented. The essence of the approach is to first develop a wavelet decomposition of the time series that retains only the statistically significant wavelet components, and to then model each such component and the residual time series as univariate autoregressive processes. The efficacy of this approach is demonstrated through the simulation of observed and paleo reconstructions of climate indices related to ENSO and AMO, tree ring and rainfall time series. Long ensemble simulations that preserve the spectral attributes of the time series in each ensemble member can be generated. The usual low order statistics are preserved by the proposed model, and its long memory performance is superior to the direction application of an autoregressive model.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.309-319
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• 2002

We consider the nonlinear autoregressive model with nonlinear ARCH errors, and find sufficient conditions for the existence of a strictly stationary process. New results are obtained, and known results are shown to emerge as special oases.