• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.2B
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• pp.163-171
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• 2009

Classical linear models have been generally used to analyze and forecast hydrologic time series. However, there is growing evidence of nonlinear structure in natural phenomena and hydrologic time series associated with their patterns and fluctuations. Therefore, the classical linear techniques for time series analysis and forecasting may not be appropriate for nonlinear processes. In recent, the BDS (Brock-Dechert-Scheinkman) statistic instead of conventional techniques has been used for detecting nonlinearity of time series. The BDS statistic was derived from the statistical properties of the correlation integral which is used to analyze chaotic system and has been effectively used for distinguishing nonlinear structure in dynamic system from random structures. DVS (Deterministic Versus Stochastic) algorithm has been used for detecting chaos and stochastic systems and for forecasting of chaotic system. This study showed the DVS algorithm can be also used for detecting nonlinearity of the time series. In this study, the stochastic and hydrologic time series are analyzed to detect their nonlinearity. The linear and nonlinear stochastic time series generated from ARMA and TAR (Threshold Auto Regressive) models, a daily streamflow at St. Johns river near Cocoa, Florida, USA and Great Salt Lake Volume (GSL) data, Utah, USA are analyzed, daily inflow series of Soyang dam and the results are compared. The results showed the BDS statistic is a powerful tool for distinguishing between linearity and nonlinearity of the time series and DVS plot can be also effectively used for distinguishing the nonlinearity of the time series.

• Journal of the Korean Data and Information Science Society
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• v.12 no.1
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• pp.71-78
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• 2001

Three test statistics are proposed for the presence of seasonality in multiplicative seasonal time series models. Further their common limiting distribution is derived under some assumptions.

• Journal of the Korean Statistical Society
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• v.26 no.3
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• pp.365-382
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• 1997

In this paper we study the behaviors of the generalized Durbin-Watson (DW) statistics when the nonstationary seasonal time series regression model is misspecified. It is observed that when the series is seasonally integrated the generalized DW statistic for the seasonal period order autocorrelation converges in probability to zero while teh generalized DW statistic for the first order autocorrelation has nondegenerate asymptotic distribution. When the series is regularly and seasonally integrated the generalized DW for the first order autocorrelation still converges in probability to zero.

• Journal of Korea Water Resources Association
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• v.31 no.6
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• pp.769-777
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• 1998

In this study, various time series are analyzed to check nonlinearities of the data. The nonlinearity of a system can be investigated by testing the randomness of the time series data. To test the randomness, four nonparametric test statistics and a new test statistic, called the BDS statistic are used and the results and the results are compared. The Brock, Dechert, and Scheinkman (BDS) statistic is originated from the statistical properties of the correlation integral which is used for searching for chaos and has been shown very effective in distinguishing nonlinear structures in dynamic systems from random structures. As a result of application to linear and nonlinear models which are well known, the BDS statistic is found to be more effective than nonparametric test statistics in identifying nonlinear structure in the time series. Hydrologic time series data are fitted to ARMA type models and the statistics are applied to the residuals. The results show that the BDS statistic can distinguish chaotic nonlinearity from randomness and that the BDS statistic can also be used for verifying the validity of the fitted model.

• Communications for Statistical Applications and Methods
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• v.12 no.2
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• pp.359-364
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• 2005

This paper considers a specification test of conditional Poisson regression model for time series count data. Although conditional models for count data have received attention and proposed in several ways, few studies focused on checking its adequacy. Motivated by the test of martingale difference assumption, a specification test via Ljung-Box statistic is proposed in the conditional model of the time series count data. In order to illustrate the performance of Ljung- Box test, simulation results will be provided.

• Communications for Statistical Applications and Methods
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• v.7 no.1
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• pp.87-96
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• 2000

Nonlinear time series prediction is derived and compared between statistic of modeling and neural network method. In particular mean squared errors of predication are obtained in generalized random coefficient model and generalized autoregressive conditional heteroscedastic model and compared with them by neural network forecasting.

• Journal of the Korean Statistical Society
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• v.26 no.3
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• pp.417-427
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• 1997

In this paper the parameter change problem in the stationary time series is considered. We propose a cumulative sum (CUSUM) of squares-type test statistic for detection of parameter changes in the AR(1) process. The proposed test statistic is based on the CUSIM of the squared observations and is shown to converge to a standard Brownian bridge. Simulations are performed to evaluate the performance of the proposed statistic and a real example is provided to illustrate the procedure.

• Journal of the Korean Data and Information Science Society
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• v.15 no.2
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• pp.441-447
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• 2004

Li and Mak (1994) developed a test statistic for detecting the non-linearity and the heteroscedasticity of the time series data. But it is well known that the test statistic may be very sensitive in case of heavy-tailed distributions of the errors. Jiang et al.(2001) suggested the robust method for ARCH models but the calculation procedures for the estimation are very complicated. We suggested the robust method based on Huber's function and our method works quite well rater than the Li and Mak(1994). Also our method is relatively easy to calculate the test statistic.

• Communications for Statistical Applications and Methods
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• v.20 no.3
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• pp.199-205
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• 2013

We employ sieve bootstraps for empirical likelihood tests in time series models because their null distributions are often vulnerable to the presence of serial dependence. We found a significant size refinement of the bootstrapped versions of a Lagrangian Multiplier type test statistic regardless of the bandwidth choice required by long-run variance estimations.

• Journal of the Korean Data and Information Science Society
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• v.17 no.1
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• pp.115-122
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• 2006

A test is suggested for detecting deviations from both multivariate normality and independence. This test can be used for assessing the normality and independence of univariate time series residuals. We derive the limiting distribution of the test statistic and a simulation study is conducted to study the accuracy of the limiting distribution in finite samples. Finally, we apply our method to a real data of time series.