Estimating long-range dependence in time series: An evaluation of estimators implemented in R

Stroe-Kunold, Esther; Stadnytska, Tetiana; Werner, Joachim; Braun, Simone

doi:10.3758/brm.41.3.909

Cited by 33 publications

(27 citation statements)

References 60 publications

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“…We performed DFA using the package 'fractal' (Constantine & Percival 2011) in R statistical software 2.11.1 (R Development Core Team 2008). In order to avoid spurious results that can arise when relying on any single fractal analytical method (Gao et al 2006, Stroe-Kunold et al 2009), we supplement our analysis by also estimating the scaling exponents of these sequences using 2 other fractal methods: power spectral density (PSD), which is one of the more commonly used methods to identify the presence of scaling behaviour (Eke et al 2000), and the madogram, which provides a robust estimate of fractal dimension (Bez & Bertrand 2011). Like αDFA, β PSD also provides information about the nature of the signal under investigation, with β ε (−1, 1) and β ε (1, 3) indicating fGn and fBm, respectively (Cannon et al 1997).…”

Section: Diving Data Analysismentioning

confidence: 99%

Corticosterone administration leads to a transient alteration of foraging behaviour and complexity in a diving seabird

Cottin¹,

MacIntosh²,

Kato³

et al. 2014

Mar. Ecol. Prog. Ser.

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Hormones link environmental stimuli to the behavioural and/or physiological responses of organisms. The release of corticosterone has major effects on both energy mobilization and its allocation among the various requirements of an individual, especially regarding survival and reproduction. We therefore examined the effects of experimentally elevated baseline corticosterone levels on the foraging behaviour of Adélie penguins Pygoscelis adeliae during chickrearing. We monitored the at-sea behaviour of corticosterone-implanted and control male birds using time-depth recorders, and monitored the effects of corticosterone treatment on their body conditions as well as their chicks' body masses and survival. Bio-logged data were examined via traditional measures of diving behaviour as well as fractal analysis as an index of behavioural complexity. Corticosterone administration caused a transient decrease in both overall foraging effort (i.e. reductions in the duration of at-sea trips, the time spent diving and the number of dives performed) and foraging complexity. In contrast, per-dive performance indices suggested an increase in both efficiency and prey pursuit rates. Ultimately, however, we observed no short-term effects of treatment on adult body condition and chick body mass and survival. We conclude that under higher corticosterone levels, sequences of behaviour may become more structured and periodic, as observed in treated birds. The increased energy allocation to dive-scale behaviours observed in treated birds might then reflect an adjustment to intrinsic constraints allowing reductions in energy expenditure at the trip-scale. This study highlights the utility of using both traditional and fractal analyses to better understand scale-dependent responses of animals to energetic and various other environmental challenges.

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Section: Diving Data Analysismentioning

confidence: 99%

Corticosterone administration leads to a transient alteration of foraging behaviour and complexity in a diving seabird

Cottin¹,

MacIntosh²,

Kato³

et al. 2014

Mar. Ecol. Prog. Ser.

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“…2, middle). The existence of such a situation is well-known in literature and usually it is referred to the fact that in analyzed time series we have longterm dependences [9]. This is especially visible if plot is done on a log-log scale (Fig.…”

Section: Results Of Experimentsmentioning

confidence: 99%

Influence of Long-Term Dependences on Hard Drives Performance during Human Computer Interaction

Strzałka

2016

Acta Phys. Pol. A

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Today, computer systems become one of the most important systems in technology and our life. They have a plenty of possible applications but most of them can be described as a transformation of (electrical) energy into useful work = calculations. This process is not so simple as it seems to be because the structure of computers hardware is very complicated and processed tasks are also very complex. Because the expectations of computer users are very high, a lot of computer resources are used only for operating systems normal work. Some existing solutions, especially in the memory system, guarantee that computer systems have acceptable performance but this parameter depends on many important system features. In this paper we will focus on one parameter, namely average disk time s/ transfer, in order to show the complex behavior of this memory system part during mancomputer interaction. This is one of the most important counters in computer systems that works under Windows family operating systems and describes measurement related to hard drive based on the complete roundtrip time of any request.

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“…For each parameter, numerous estimators have been developed, but there is no clear winner among them (Stroe-Kunold et al, 2009; Stadnytska et al, 2010; Stadnitski, 2012). Furthermore, statistical characteristics of some non-fractal empirical structures can resemble those of 1/ f noise, which may cause erroneous classifications (Wagenmakers et al, 2004; Thornton and Gilden, 2005).…”

Section: Measuring Fractalitymentioning

confidence: 99%

Measuring Fractality

Stadnitski¹

2012

Front. Physio.

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When investigating fractal phenomena, the following questions are fundamental for the applied researcher: (1) What are essential statistical properties of 1/f noise? (2) Which estimators are available for measuring fractality? (3) Which measurement instruments are appropriate and how are they applied? The purpose of this article is to give clear and comprehensible answers to these questions. First, theoretical characteristics of a fractal pattern (self-similarity, long memory, power law) and the related fractal parameters (the Hurst coefficient, the scaling exponent α, the fractional differencing parameter d of the autoregressive fractionally integrated moving average methodology, the power exponent β of the spectral analysis) are discussed. Then, estimators of fractal parameters from different software packages commonly used by applied researchers (R, SAS, SPSS) are introduced and evaluated. Advantages, disadvantages, and constrains of the popular estimators (dMathClass-op^ML, power spectral density, detrended fluctuation analysis, signal summation conversion) are illustrated by elaborate examples. Finally, crucial steps of fractal analysis (plotting time series data, autocorrelation, and spectral functions; performing stationarity tests; choosing an adequate estimator; estimating fractal parameters; distinguishing fractal processes from short-memory patterns) are demonstrated with empirical time series.

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Estimating long-range dependence in time series: An evaluation of estimators implemented in R

Cited by 33 publications

References 60 publications

Corticosterone administration leads to a transient alteration of foraging behaviour and complexity in a diving seabird

Corticosterone administration leads to a transient alteration of foraging behaviour and complexity in a diving seabird

Influence of Long-Term Dependences on Hard Drives Performance during Human Computer Interaction

Measuring Fractality

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