Components of multifractality in the central England temperature anomaly series

Souza, Jeferson de; Queirós, Sı́lvio M. Duarte; Grimm, Alice M.

doi:10.1063/1.4811546

Cited by 8 publications

(2 citation statements)

References 50 publications

(16 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Multifractality [1,2,3,4,5,6,7] is commonly considered as very interesting feature of complex and composite systems which attracts a lot of attention in many areas of science. The multifractal properties of time series are extensively studied because of their omnipresence in various phenomena in nature connected with complexity like turbulence [8,9], astronomy [10], climate phenomena [11,12,13], physiology [14], text structure [15,16,17,18], physics [19,20] or finances [21,22,23,24,25,26,27,28,29,30,31,32,33,34,35]. This fragmentary list is far from being exhaustive and does not cover enormous number of publications on the subject.…”

Section: Introductionmentioning

confidence: 99%

Quantitative approach to multifractality induced by correlations and broad distribution of data

Rak

Grech

2018

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

We analyze quantitatively the effect of spurious multifractality induced by the presence of fat-tailed symmetric and asymmetric probability distributions of fluctuations in time series. In the presented approach different kinds of symmetric and asymmetric broad probability distributions of synthetic data are examined starting from Levy regime up to those with finite variance. We use nonextensive Tsallis statistics to construct all considered data in order to have good analytical description of frequencies of fluctuations in the whole range of their magnitude and simultaneously the full control over exponent of power-law decay for tails of probability distribution. The semi-analytical compact formulas are then provided to express the level of spurious multifractality generated by the presence of fat tails in terms of Tsallis parameterq and the scaling exponent β of the asymptotic decay of cumulated probability density function (CDF). The results are presented in Hurst and Hölder languages -more often used in study of multifractal phenomena. According to the provided semi-analytical relations, it is argued how one can make a clear quantitative distinction for any real data between true multifractality caused by the presence of nonlinear correlations, spurious multifractality generated by fat-tailed shape of distributions -eventually with their asymmetry, and the correction due to linear autocorrelations in analyzed time series of finite length. In particular, the spurious multifractal effect of fat tails is found basic for proper quantitative estimation of all spurious multifractal effects. Examples from stock market data are presented to support these findings.

show abstract

Section: Introductionmentioning

confidence: 99%

Quantitative approach to multifractality induced by correlations and broad distribution of data

Rak

Grech

2018

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

show abstract

“…These are some of the reasons for the interest shown in attempting to determine the minimum time span required to detect a long-term trend signal. In climatological terms, this would allow the separation of the trend (signal) from the noise (natural variability and cycles), with a relative contribution from each of these variable components depending on the time scale chosen (De Souza et al, 2013;Münch and Laepple, 2018).…”

Section: Introductionmentioning

confidence: 99%

Temporal variations of trends in the Central England Temperature series

Gonzalez‐Hidalgo

Peña‐Angulo

Beguerı́a

2020

CIG

View full text Add to dashboard Cite

Variations in trend rates of annual values of the Central England Temperature series (CET) over the period1659-2017 were analysed using moving windows of different length, to identify the minimum period in which the trend expresses a climate signal not hidden by the noise produced by natural variability. Trend rates exhibit high variability and irregular shifting from positive to negative values unless very long window lengths (of 100 years or more) are used. In general, as the duration of the length of the temporal window analysed increases, the absolute range of the trend rates decreases and the signal-to-noise (S/N) ratio increases. The relationship between the S/N ratio and the window length also depended on the total length of the series, so high S/N values are achieved faster when shorter time series are considered. This prevents suggesting a minimum window length for undertaking trend analyses.A comparison between CET and the average continental series in the Berkeley Earth Surface Temperature (BEST) database in their overlapping period (1753-2017) repeats the patterns described for 1659-2017, although the average values of the rates, ranges and the "threshold period" in years change, and are more variable in CET than in BEST.Analysis of both series suggests that the recent warming started early and can be linked to the recovery of temperatures after the Little Ice Age. This process has characterised by progressively increasing trend rates, but also includes periods of deceleration or even negative trends spanning less than 50 years. The behaviour of the two long-term temperature records analysed agrees with a long-term persistence (LTP) process. We estimated the Hurst exponent of the CET series to be around 0.72 and 0.8, which reinforces the LTP hypothesis. This implies that the currently widespread statistical framework assuming a stationary, short-memory process in which departures from the norm can be easily assessed by monotonic trend analysis should not be accepted for long climatic series. In brief, relevant questions relative to the recent evolution of temperatures such as the distinction between natural variability and departures from stationarity; attribution of the causes of variability at different time scales; determination of the shortest window length to detect a trend; and other similar ones have still not been answered and may require adoption of an alternative analytical framework.

show abstract

Measuring multiscaling in financial time-series

Buonocore

Aste

Matteo

2016

Chaos, Solitons & Fractals

View full text Add to dashboard Cite

We discuss the origin of multiscaling in financial time-series and investigate how to best quantify it. Our methodology consists in separating the different sources of measured multifractality by analysing the multi/uni-scaling behaviour of synthetic time-series with known properties. We use the results from the synthetic time-series to interpret the measure of multifractality of real log-returns timeseries. The main finding is that the aggregation horizon of the returns can introduce a strong bias effect on the measure of multifractality. This effect can become especially important when returns distributions have power law tails with exponents in the range [2,5]. We discuss the right aggregation horizon to mitigate this bias.

show abstract

Components of multifractality in the central England temperature anomaly series

Cited by 8 publications

References 50 publications

Quantitative approach to multifractality induced by correlations and broad distribution of data

Quantitative approach to multifractality induced by correlations and broad distribution of data

Temporal variations of trends in the Central England Temperature series

Measuring multiscaling in financial time-series

Contact Info

Product

Resources

About