The BDS statistic and residual test

Kim, H. S.; Kang, Dongwoo; Kim, J. H.

doi:10.1007/s00477-002-0118-0

Cited by 51 publications

(27 citation statements)

References 9 publications

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“…If the sample size is fixed, we expect the finite sample property to worsen as "m" increases. This study follows the recommendation of [22] for selecting the ranges of m, r, N. Therefore, 500 or more observations are prepared and the embedding dimension m is used in the range of 2 5 m ≤ ≤ . Then, the value of "r" is selected as the half standard deviations of the data sets.…”

Section: Nonlinearity For Tree-ring and Soi Seriesmentioning

confidence: 99%

Hurst’s Memory for Chaotic, Tree Ring, and SOI Series

Kim¹,

Kim²,

Min³

2014

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Hurst's memory that roots in early work of the British hydrologist H.E. Hurst remains an open problem in stochastic hydrology. Today, the Hurst analysis is widely used for the hydrological studies for the memory and characteristics of time series and many methodologies have been developed for the analysis. So, there are many different techniques for the estimation of the Hurst exponent (H). However, the techniques can produce different characteristics for the persistence of a time series each other. This study uses several techniques such as adjusted range, rescaled range (RR) analysis, modified rescaled range (MRR) analysis, 1/f power spectral density analysis, Maximum Likelihood Estimation (MLE), detrended fluctuations analysis (DFA), and aggregated variance time (AVT) method for the Hurst exponent estimation. The generated time series from chaos and stochastic systems are analyzed for the comparative study of the techniques. Then, this study discusses the advantages and disadvantages of the techniques and also the limitations of them. We found that DFA is the most appropriate technique for the Hurst exponent estimation for both the short term memory and long term memory. We analyze the SOI (Southern Oscillations Index) and 6 tree-ring series for USA sites by means of DFA and the BDS statistic is used for nonlinearity test of the series. From the results, we found that SOI series is nonlinear time series which has a long term memory of H = 0.92. Contrary to earlier work, all the tree ring series are not random from our analysis. A certain tree ring series show a long term memory of H = 0.97 and nonlinear property. Therefore, we can say that the SOI series has the properties of long memory and nonlinearity and tree ring series could also show long memory and non-linearity.

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Section: Nonlinearity For Tree-ring and Soi Seriesmentioning

confidence: 99%

Hurst’s Memory for Chaotic, Tree Ring, and SOI Series

Kim¹,

Kim²,

Min³

2014

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“…그러나 이들 기존의 방법들은 비선형 특성을 지닌 시계열에 대해서는 제대 로 검토하지 못함이 밝혀지고 있다 (Kim et al, 2003). (Rodriguez-Iturbe et al, 1989;Wilcox et al, 1991;Mindlin and Gilmore, 1992;Sangoyomi et al, 1996;Kim et al 1998Kim et al , 2001Bouzata et al 2004) …”

Section: 서 론unclassified

Influence of Noise on Chaotic Time Series

Choi¹,

Lee²,

Kim³

2009

Journal of Korea Water Resources Association

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The purpose of this paper is to investigate the influence of noise on chaotic time series. We used two time series of Lorenz system and of Great Salt Lake's volume data which are well known as chaotic systems. This study investigated the attractors, correlation dimensions, and Close Returns Plots and Close Returns Histograms of two time series to investigate the influence of noise as increasing noise level. We performed Chi-square test to the relative frequency of Close Returns Histogram from Close Returns Plot for the investigation of stochastic process of chaotic time series as increasing noise level of time series. As the results, two time series were changed from chaotic to stochastic series as noise level is increased. Finally, we analyzed the effect of noise cancellation by using Simple Moving Average method. The results of applications of Simple Moving Average method to Lorenz and GSL time series showed that we could effectively cancel the noise. Then we could confirm the applicability of Simple Moving Average method to cancel the noise for the hydrologic time series having chaotic characteristics.

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“…그에 따라서, 최근 에는 추계학적 특성을 반영할 수 있는 Tree-ring 연구가 이 루어지기도 하였으나 (Devineni et al, 2013;Gray et al, 2004;Raffalli-Delerce et al, 2004;Stoffel and Bollschweiler, 2009), 최근까지도 선형적인 가정에 기반을 둔 재생성 기법 이 많이 사용되었다 (Akkemik et al, 2005;Brázdil et al, 2002;Salzer and Kipfmueller, 2005;Woodhouse, 2001;Wilson and Luckman, 2002;Xuemei and Xiangding, 1997 (Battiti, 1989, Giill et al, 1981. Brock et al, 1991;Brock et al, 1996;Kim et al, 2003). (Salas et al, 1993).…”

Section: Introduction 1)unclassified

Annual Precipitation Reconstruction Based on Tree-ring Data at Seorak

Kwak¹,

Han²,

Lee³

et al. 2015

Journal of Korean Society on Water Environment

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The purpose of this research is reconstruction of annual precipitation based on Tree-ring series at Seorak mountain and examine its effectiveness. To do so we performed nonlinear time series characteristics test of Tree-ring series and reconstructed annual precipitation of Gangneung from 1687 to 1911 using Artificial neural network and Nonlinear autoregressive exogeneous input (NARX) model which reflects stochastic properties. As a result, Tree-ring series at Seorak Mountain shows nonlinear time series property and reconstructed annual precipitation series drawn from NARX is similar in statistical characteristics of observed annual time series.

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The BDS statistic and residual test

Cited by 51 publications

References 9 publications

Hurst’s Memory for Chaotic, Tree Ring, and SOI Series

Hurst’s Memory for Chaotic, Tree Ring, and SOI Series

Influence of Noise on Chaotic Time Series

Annual Precipitation Reconstruction Based on Tree-ring Data at Seorak

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