A multifractal detrended fluctuation description of Iranian rial–US dollar exchange rate

Norouzzadeh, Payam; Rahmani, Bahareh

doi:10.1016/j.physa.2005.11.019

Cited by 155 publications

(72 citation statements)

References 30 publications

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“…Similar phenomena are observed for exponential distributions in the partition function framework [51]. To understand the impact of the distribution, one can either remove the large positive and negative returns [52] or generate surrogate data having a Gaussian distribution while keeping the linear correlation of the original data [26,27,53]. In this Letter, we will systematically investigate these factors together with a new factor reflecting possible hidden patterns in the raw time series.…”

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confidence: 80%

The components of empirical multifractality in financial returns

2009

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Abstract. -We perform a systematic investigation on the components of the empirical multifractality of financial returns using the daily data of Dow Jones Industrial Average from 26 May 1896 to 27 April 2007 as an example. The temporal structure and fat-tailed distribution of the returns are considered as possible influence factors. The multifractal spectrum of the original return series is compared with those of four kinds of surrogate data: (1) shuffled data that contain no temporal correlation but have the same distribution, (2) surrogate data in which any nonlinear correlation is removed but the distribution and linear correlation are preserved, (3) surrogate data in which large positive and negative returns are replaced with small values, and (4) surrogate data generated from alternative fat-tailed distributions with the temporal correlation preserved. We find that all these factors have influence on the multifractal spectrum. We also find that the temporal structure (linear or nonlinear) has minor impact on the singularity width ∆α of the multifractal spectrum while the fat tails have major impact on ∆α, which confirms the earlier results. In addition, the linear correlation is found to have only a horizontal translation effect on the multifractal spectrum in which the distance is approximately equal to the difference between its DFA scaling exponent and 0.5. Our method can also be applied to other financial or physical variables and other multifractal formalisms.Introduction. -There are a wealth of studies showing that financial markets exhibit multifractal nature [1][2][3]. Many different methods have been applied to characterize the hidden multifractal behavior in finance, for instance, the fluctuation scaling analysis [4][5][6], the structure function (or height-height correlation function) method [1,[7][8][9][10][11][12][13][14][15][16][17], the multiplier method [18], the multifractal detrended fluctuation analysis (MF-DFA) [19][20][21][22][23][24][25][26][27], the partition function method [28][29][30][31][32][33][34][35][36][37][38], the wavelet transform approaches [39][40][41][42], to list a few. There are also efforts seeking for applications of the extracted multifractal spectra. Some researchers reported that the observed multifractal singularity spectrum has predictive power for price fluctuations [29,31,38], can serve as a measure of market risk by introducing a new concept termed multifractal volatility [35], and can be used to quantify the inefficiency of markets [43].

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confidence: 80%

The components of empirical multifractality in financial returns

2009

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“…It should be noted that this parameter is identical to the width of the singularity spectrum f ðaÞ at f ¼ 0. A wider singularity spectrum indicates a richer multifractality (Norouzzadeh and Rahmani 2006a, b).…”

Section: Multifractal Detrended Fluctuation Analysis (Mfdfa)mentioning

confidence: 99%

“…Following that, Kantelhardt et al (2002) extended DFA into multifractal detrended fluctuation analysis (MFDFA) which enables the multifractal behavior of data to be detected, and by studying their shuffled and surrogate time series and comparing them with the results of the original series, the sources of multifractality can be investigated (Jafari et al 2007; Kimiagar et al 2009;Lim et al 2007;Niu et al 2008;Pedram and Jafari 2008;Telesca et al 2004). MFDFA has been used to study time series in geophysics (Kantelhardt et al 2003;Kavasseri and Nagarajan 2005;Koscielny-Bunde et al 2006), physiology (Dutta 2010;Makowiec et al 2006Makowiec et al , 2011, financial markets (Oswiecimka et al 2005;Yuan et al 2009), and the exchange rates of currencies (Norouzzadeh and Rahmani 2006a, b;Oh et al 2012;Wang et al 2011a, b). Multifractals describe the dynamic characteristics of systems more carefully and comprehensively, and characterize their properties both locally and globally.…”

Section: Introductionmentioning

confidence: 99%

Multifractal analysis of the drought area in seven large regions of China from 1961 to 2012

Hou

Feng

Yan

et al. 2017

Meteorol Atmos Phys

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Based on a monthly drought index, the Standardized Precipitation Index (SPI), we investigate the multifractality of monthly drought areas in seven major regions in China from 1961 to 2012 using multifractal detrended fluctuation analysis. The results show that multifractality is evident in the monthly time series for all seven regions, but its strength varies between areas. From the numerical results, we further examine the stationarity and persistence of the time series in the seven drought areas. The characteristics of the variance of big and small fluctuations are also analyzed. The characteristics of multifractal spectra are used to distinguish the features of the singularity of all the data, as well as the large and small fluctuations and the spread of the changes of fractal patterns, and so on, in the monthly drought area time series for the different regions. Finally, we investigate the possible source(s) of multifractality in the drought series by random shuffling as well as surrogating the original series for each region.

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“…Work on higher-frequency dat a [23,45] has found that the correlations are the most likely cause of mult ifract ality. Mixed result s have been found for foreign exchange rat es [46,51,52]. T hese varied result s imply t hat the main source of multifractality is dependent on the part iculars of each specific dat a set and t hat t here is no universal law.…”

Section: Source Of Scaling -Dist Ribut Ionmentioning

confidence: 99%

The origins of multifractality in financial time series and the effect of extreme events

2014

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Abst ract . T his paper present s t he result s of mult ifract al t est ing of two set s of financial dat a: daily dat a of t he Dow J ones Indust rial Average (DJ IA) index and minut ely dat a of t he Euro St oxx 50 index. W here mult ifract al scaling is found, t he spect rum of scaling exponent s is calculat ed via Mult ifract al Det rended F luct uat ion Analysis. In bot h cases, furt her invest igat ions reveal t hat t he t emporal correlat ions in t he dat a are a more significant source of t he mult ifract al scaling t han are t he dist ribut ions of t he ret urns. It is also shown t hat t he ext reme event s which make up t he heavy t ails of t he dist ribut ion of t he Euro St oxx 50 log ret urns dist ort t he scaling in t he dat a set . T he most ext reme event s are inimical t o t he scaling regime. T his result is in cont rast t o previous findings t hat ext reme event s cont ribut e t o mult ifract ality. Int roduct ionMult ifract al analysis has proved t o be a valuable met hod of capt uring t he underlying scaling st ruct ure present in many types of syst ems via generalised dimensions [1] and f (α) spect ra [2]. T hese syst ems include diff usion limit ed aggregat ion [3][4][5], fluid flow t hrough random porous media [6], at omic spect ra of rare-eart h element s [7], clust erclust er aggregat ion [8] and t urbulent flow [9]. In physiology, mult ifract al st ruct ures have been found in heart rat e variability [10] and brain dynamics [11], and mult ifract al analysis has been helpful in dist inguishing between healthy and pathological patients [12]. Mult ifract al measures have also been found in man-made phenomena such as t he Int ernet [13], art [14] and the stock market [15][16][17].T he concept of mult ifract ality was first int roduced in t he cont ext of t urbulence. It was soon applied t o finance because of it s heavy t ails and long-t erm dependence. T hese two feat ures are also argued t o be present in financial dat a [18,19]. P erforming mult ifract al analysis helps t o increase our knowledge about t he financial syst em and furt her charact erise it . Many st udies have found mult ifract al scaling in financial dat a [20][21][22][23]. An underst anding of t his mult ifract al st ruct ure can enable deeper underst anding of t he dynamics of financial market s. If it is found t o be a universal feat ure of financial dat a, it provides an addit ional benchmark by which t o measure t he fitness of financial models. This in turn can help in the design of well performing port folios and in risk management [17]. a e-mail: elena.s.green@nuim.ieThe Multifractal Model of Asset Returns (MMAR) was int roduced by Mandelbrot et al. [24] as an explanat ion of t he volat ility clust ers in financial dat a and t o include "out liers", large deviat ions which make up t he fat t ails of t he ret urn dist ribut ion. T he MMAR was present ed as an alt ernat ive t o Aut oregressive Condit ional Het eroscedast icity (ARCH) models which were int roduced by Engle [25] t o account for volat ility clust er...

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A multifractal detrended fluctuation description of Iranian rial–US dollar exchange rate

Cited by 155 publications

References 30 publications

The components of empirical multifractality in financial returns

The components of empirical multifractality in financial returns

Multifractal analysis of the drought area in seven large regions of China from 1961 to 2012

The origins of multifractality in financial time series and the effect of extreme events

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