Long‐range dependence

Beran, Jan

doi:10.1002/wics.52

Cited by 20 publications

(14 citation statements)

References 155 publications

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“…Numerous estimation methods have been developed for this purpose, including the Hurst rescaled range analysis, Higuchi's method, Geweke and Porter-Hudak's method, Whittle's maximum likelihood estimator, detrended fluctuation analysis, and others (Taqqu et al, 1995;Montanari et al, 1997Montanari et al, , 1999Rea et al, 2009;Stroe-Kunold et al, 2009). For brevity, these methods are not elaborated here; readers are referred to Beran (2010) and Witt and Malamud (2013) for details. While these estimation methods have been extensively adopted, they are unfortunately only applicable to regular (i.e., evenly spaced) data, e.g., daily streamflow discharge, monthly temperature.…”

Section: Motivation and Objective Of This Workmentioning

confidence: 99%

“…Although the short-term memory assumption holds sometimes, it cannot adequately describe many time series whose ACFs decay as a power law (thus much slower than exponentially) and may not reach zero even for large lags, which implies that the ACF is non-summable. This property is commonly referred to as long-term memory or fractal scaling, as opposed to short-term memory (Beran, 2010).…”

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confidence: 99%

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Evaluation of statistical methods for quantifying fractal scaling in water-quality time series with irregular sampling

Zhang

Harman

Kirchner

2018

Hydrol. Earth Syst. Sci.

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Abstract. River water-quality time series often exhibit fractal scaling, which here refers to autocorrelation that decays as a power law over some range of scales. Fractal scaling presents challenges to the identification of deterministic trends because (1) fractal scaling has the potential to lead to false inference about the statistical significance of trends and (2) the abundance of irregularly spaced data in water-quality monitoring networks complicates efforts to quantify fractal scaling. Traditional methods for estimating fractal scalingin the form of spectral slope (β) or other equivalent scaling parameters (e.g., Hurst exponent) -are generally inapplicable to irregularly sampled data. Here we consider two types of estimation approaches for irregularly sampled data and evaluate their performance using synthetic time series. These time series were generated such that (1) they exhibit a wide range of prescribed fractal scaling behaviors, ranging from white noise (β = 0) to Brown noise (β = 2) and (2) their sampling gap intervals mimic the sampling irregularity (as quantified by both the skewness and mean of gap-interval lengths) in real water-quality data. The results suggest that none of the existing methods fully account for the effects of sampling irregularity on β estimation. First, the results illustrate the danger of using interpolation for gap filling when examining autocorrelation, as the interpolation methods consistently underestimate or overestimate β under a wide range of prescribed β values and gap distributions. Second, the widely used Lomb-Scargle spectral method also consistently underestimates β. A previously published modified form, using only the lowest 5 % of the frequencies for spectral slope estimation, has very poor precision, although the overall bias is small. Third, a recent wavelet-based method, coupled with an aliasing filter, generally has the smallest bias and root-meansquared error among all methods for a wide range of prescribed β values and gap distributions. The aliasing method, however, does not itself account for sampling irregularity, and this introduces some bias in the result. Nonetheless, the wavelet method is recommended for estimating β in irregular time series until improved methods are developed. Finally, all methods' performances depend strongly on the sampling irregularity, highlighting that the accuracy and precision of each method are data specific. Accurately quantifying the strength of fractal scaling in irregular water-quality time series remains an unresolved challenge for the hydrologic community and for other disciplines that must grapple with irregular sampling.

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Section: Motivation and Objective Of This Workmentioning

confidence: 99%

mentioning

confidence: 99%

Evaluation of statistical methods for quantifying fractal scaling in water-quality time series with irregular sampling

Zhang

Harman

Kirchner

2018

Hydrol. Earth Syst. Sci.

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“…Here we provide a review of the definitions of such processes and several typical modeling approaches, including both time-domain and frequency-domain techniques, with special attention to their reconciliation. For a more comprehensive review, readers are referred to Beran et al (2013), Boutahar et al (2007), and Witt and Malamud (2013). Strictly speaking, X t is called a stationary long-memory process if the condition lim k→∞ k α γ (k) = C 1 > 0,…”

Section: Overview Of Approaches For Quantification Of Fractal Scalingmentioning

confidence: 99%

Authors' response to referee #2

Zhang¹

2017

Preprint

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“…so-called long-memory processes; see e.g. [2][3][4]). It is well known that different geophysical time series (hydrometeorological ones inclusive) reveal different values of the Hurst exponent, usually greater than 0.5 (for further details see [5][6][7]), which means that investigators should seriously consider using such models that are, moreover, capable of capturing the hyperbolic decay of the autocorrelation function, as described in [8].…”

Section: Introductionmentioning

confidence: 99%

Freely available daily hydrometeorological data from Czechia: further insights

Ledvinka

Jedlicka

2018

E3S Web Conf.

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Abstract. Quite recently, freely available mean daily discharge series representing the territory of Czechia were complemented by ten daily series of nine climate variables, spanning usually from 1961 to the present. Their length thus allows the analyses similar to those conducted approximately a year ago in relation to the long series of discharge. Besides this possibility, the current paper goes further and shows how these long series (including discharge) can be used in order to assess the presence of the so-called Hurst phenomenon. Using a wavelet-based approach, several important differences in the wavelet spectra and values of the Hurst exponent (as well as the uncertainty in their estimation) were found when focusing on discharge, air temperature and precipitation. Furthermore, using the stationarity and unit root tests, it was revealed that, unlike precipitation, air temperature and discharge series may be characterized by long-memory processes in many cases. Finally, as the paper is devoted mainly to students, a short R script is presented in Appendix that makes it easier to work with the online files offered by Czech climatologists.

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Long‐range dependence

Cited by 20 publications

References 155 publications

Evaluation of statistical methods for quantifying fractal scaling in water-quality time series with irregular sampling

Evaluation of statistical methods for quantifying fractal scaling in water-quality time series with irregular sampling

Authors' response to referee #2

Freely available daily hydrometeorological data from Czechia: further insights

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