• 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.

• Journal of Wetlands Research
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• v.21 no.1
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• pp.66-76
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• 2019

Recently, natural disasters such as floods and droughts are frequently occurred due to climate change and the damage is also increasing. Wetland is known to play an important role in reducing and minimizing the damage. In particular, water level variability needs to be analyzed in order to understand the various functions of wetland as well as the reduction of damage caused by natural disaster. Therefore, in this study, we fitted water level series of Upo wetland in Changnyeong, Gyeongnam province to a proper time series model and residual test was performed to confirm the appropriateness of the model. In other words, ARIMA model was constructed and its residual tests were performed using existing nonparametric statistics, BDS statistic, and Close Returns Histogram(CRH). The results of residual tests were compared and especially, we showed the applicability of CRH to analyze the residuals of time series model. As a result, CRH produced not only accurate randomness test result, but also produced result in a simple calculation process compared to the other methods. Therefore, we have shown that CRH and BDS statistic can be effective tools for analyzing residual in time series model.

• Genomics & Informatics
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• v.21 no.1
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• pp.1.1-1.1
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• 2023

• KSCE Journal of Civil and Environmental Engineering Research
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• v.31 no.1B
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• pp.37-45
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• 2011

We studied noise influence on nonlinear chaotic system by using Logistic data series which is known as a typical nonlinear chaotic system. We regenerated Logistic data series by the method of adding noise according to noise level. And, we performed some analyses such as phase space reconstruction, correlation dimension, BDS statistics, and DVS Algorithms which are known as the methods of nonlinear deterministic or chaotic analysis. If we see the results of analysis, the characteristics of data series are gradually changed from nonlinear chaotic data series to random stochastic data series according to increasing noise level. We applied Low Pass Filter (LPF) and Kalman Filter techniques for the investigation of removing effect of the added noise to data series. Typical nonparametric method cannot distinguish nonlinear random series but the BDS statistic can distinguish the nonlinear randomness of the time series. Therefore this study used the BDS statistic which is well known as nonlinear statistical method for the investigation of randomness of time series for the effect of removing noise of data series. We found that Kalman filter is better method to remove the noise of chaotic data series even for high noise level.

• Journal of Korea Water Resources Association
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• v.39 no.12 s.173
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• pp.997-1012
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• 2006

We have presented a nonparametric stochastic approach for the SOI(Southern Oscillation Index) series that used nonlinear methodology called Nonlinear AutoRegressive(NAR) based on conditional kernel density function and CAFPE(Corrected Asymptotic Final Prediction Error) lag selection. The fitted linear AR model represents heteroscedasticity, and besides, a BDS(Brock - Dechert - Sheinkman) statistics is rejected. Hence, we applied NAR model to the SOI series. We can identify the lags 1, 2 and 4 are appropriate one, and estimated conditional mean function. There is no autocorrelation of residuals in the Portmanteau Test. However, the null hypothesis of normality and no heteroscedasticity is rejected in the Jarque-Bera Test and ARCH-LM Test, respectively. Moreover, the lag selection for conditional standard deviation function with CAFPE provides lags 3, 8 and 9. As the results of conditional standard deviation analysis, all I.I.D assumptions of the residuals are accepted. Particularly, the BDS statistics is accepted at the 95% and 99% significance level. Finally, we split the SOI set into a sample for estimating themodel and a sample for out-of-sample prediction, that is, we conduct the one-step ahead forecasts for the last 97 values (15%). The NAR model shows a MSEP of 0.5464 that is 7% lower than those of the linear model. Hence, the relevance of the NAR model may be proved in these results, and the nonparametric NAR model is encouraging rather than a linear one to reflect the nonlinearity of SOI series.

• The Journal of Asian Finance, Economics and Business
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• v.8 no.3
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• pp.139-154
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• 2021

This study's impetus is to explore fresh evidence to answer the question, i.e., whether remittances asymmetrically influence financial development in Bangladesh from 1975 to 2019. The study employs several tests, i.e., nonlinear unit root test, Autoregressive Distributed Lagged (ARDL), NARDL, and asymmetric causality test for establishing the pattern of association. Nonlinear unit root tests confirm that variables follow a nonlinear system of being stationary after the first difference. nonlinearity among variables is investigated by performing the BDS test and nonlinear OLS. Directional causality is investigated through both linear and nonlinear effects of remittance inflows by following the non-granger casualty test. The test statistics of Fpass and tBDM showed the Long-run cointegration in the empirical model and positive effect running from remittances inflow to financial development both in the long-run and short-run. Furthermore, the results of a standard Wald test divulge the presence of long-run and short-run asymmetry. Asymmetry causality test established unidirectional causality due to positive and negative shocks in remittances inflows to Bank-based financial development and feedback hypothesis hold for explaining causality between positive and negative shocks in remittance inflows and Stock-based financial development.