Modeling long-range cross-correlations in two-component ARFIMA and FIARCH processes

Podobnik, Boris; Horvatić, Davor; Ng, Alfonso Lam; Stanley, H. Eugene; Ivanov, Plamen Ch.

doi:10.1016/j.physa.2008.01.062

Cited by 136 publications

(45 citation statements)

References 25 publications

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“…In conclusion, cross-correlations are found in a number of studies including nanodevices [41][42][43], atmospheric geophysics [44], seismology [45], and finance [6,7,23,24,[46][47][48][49][50][51][52][53][54][55]. We study cross-correlations in both temporal and spatial collective modes using time-lag RMT (TLRMT).…”

Section: -P3mentioning

confidence: 99%

Time-lag cross-correlations in collective phenomena

Podobnik

Wang

Horvatić

et al. 2010

EPL

208

110

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PACS 89.75.Da -Systems obeying scaling laws PACS 89.90.+n -Other topics in areas of applied and interdisciplinary physics Abstract -We study long-range magnitude cross-correlations in collective modes of real-world data from finance, physiology, and genomics using time-lag random matrix theory. We find longrange magnitude cross-correlations i) in time series of price fluctuations, ii) in physiological time series, both healthy and pathological, indicating scale-invariant interactions between different physiological time series, and iii) in ChIP-seq data of the mouse genome, where we uncover a complex interplay of different DNA-binding proteins, resulting in power-law cross-correlations in xij, the probability that protein i binds to gene j, ranging up to 10 million base pairs. In finance, we find that the changes in singular vectors and singular values are largest in times of crisis. We find that the largest 500 singular values of the NYSE Composite members follow a Zipf distribution with exponent ≈ 2. In physiology, we find statistically significant differences between alcoholic and control subjects.

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Section: -P3mentioning

confidence: 99%

Time-lag cross-correlations in collective phenomena

Podobnik

Wang

Horvatić

et al. 2010

EPL

208

110

View full text Add to dashboard Cite

show abstract

“…In order to investigate the validity and performance of the proposed MM-DCCA algorithms, we perform extensive numerical experiments using uniformly distributed random number series, two-component autoregressive fractionally integrated moving average (ARFIMA) processes [35,36], Cauchy distributed random number series, and binomial measures generated from the multiplicative p-model [37]. It is known to us that there should be no cross-correlations between uniformly distributed random number series.…”

Section: Numerical Experiments With Mm-dccamentioning

confidence: 99%

“…For the two-component ARFIMA processes discussed below, we take Z = X or Y . The two-component ARFIMA process is defined as follows [36]:…”

Section: Numerical Experiments With Mm-dccamentioning

confidence: 99%

Multiscale multifractal detrended cross-correlation analysis of traffic flow

Yin

Shang

2015

Nonlinear Dyn

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In this paper, we introduce a method called multiscale multifractal detrended cross-correlation analysis (MM-DCCA) to describe the cross-correlation properties depend on the timescale in which the multifractality is computed. For traffic time series, we show that the fractal properties of cross-correlations have a relationship with the range of scale indicating the great necessity to study the cross-correlation properties between two time series at multiple scales. MM-DCCA gains a new insight into measuring different fractal properties of the cross-correlations between traffic series by sweeping all the range of scale, and it provides much richer information than multifractal detrended cross-correlation analysis (MF-DCCA). The Hurst surfaces present multifractal properties and strong long-range persistent cross-correlations between traffic series. By comparing Hurst surfaces before and after removing dominant periodicities, we find that periodicity is not the only reason which causes the crossover and dominates the cross-correlation. There are other interesting factors or underlying traffic mechanisms containing in the cross-correlation between traffic series. Moreover, the cross-correlation between the whole traffic series can be considered as a combination of both weekday and weekend parts. The results also suggest that the different periodic patterns hidden in the weekday and weekend patterns are the main distinction between them and play an important role in the Hurst surface of cross-correlation investigation.

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“…The DFA method invented by Peng et al has become a widely-used method for the determination and detection of long-range correlations in time series [25][26][27]. In order to quantify loge-range cross-correlations between two non-stationary time series, a new method called DCCA, has been proposed recently [28][29][30]. In our work, we investigate the cross-correlations of the daily price fluctuations of six different stocks in global stock markets during the period 2002-2009.…”

Section: Introductionmentioning

confidence: 99%

The cross-correlations of stock markets based on DCCA and time-delay DCCA

2011

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In this paper, the Detrended Fluctuation Analysis (DFA) and Detrended Cross-Correlation Analysis (DCCA) are used to investigate the stock markets. The DFA method is a widely-used method for the determination and detection of long-range correlations in stock time series. DCCA is a recently developed method to quantify the cross-correlations of two non-stationary time series. We report the results of correlation and cross-correlation behaviors in US and Chinese stock markets by using the DFA and DCCA methods, respectively. The DCCA shows that there exists some crossovers in the cross-correlation fluctuation function versus time scale of stock absolute returns. The cross-correlations in Chinese stock markets are stronger than those between Chinese and US stock markets. After documenting the equal-time cross-correlations using DCCA method, we study the dynamics of cross-correlations of stock series based on a time-delay. The time-dependence of the underlying cross-correlations is monitored using a time window by step of 1 day. An interesting finding is that the cross-correlation exponents and crossovers demonstrate periodical uncertainty changing with the timedelay.

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Modeling long-range cross-correlations in two-component ARFIMA and FIARCH processes

Cited by 136 publications

References 25 publications

Time-lag cross-correlations in collective phenomena

Time-lag cross-correlations in collective phenomena

Multiscale multifractal detrended cross-correlation analysis of traffic flow

The cross-correlations of stock markets based on DCCA and time-delay DCCA

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