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1
Content available remote

Alternative Random Matrix Approach in Analysis of Correlations in Financial Data

100%
Sawa M., Grech D.
Acta Physica Polonica A
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2015
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vol. 127
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issue 3A
A-118-A-122
EN
We present an alternative method based on random matrix approach that enables to distinguish the respective role of temporal autocorrelations inside given time series and cross correlations between various time series. The proposed algorithm is based on the properties of Wigner eigenspectrum of random matrices instead of commonly used Wishart eigenspectrum methodology. It is then qualitatively and quantitatively applied to financial data of stocks building WIG 30 - the main Warsaw Stock Exchange Index.
2
Content available remote

Report on Foundation and Organization of Econophysics Graduate Courses at Faculty of Physics of University of Warsaw and Department of Physics and Astronomy of the Wrocław University

100%
Kutner R., Grech D.
Acta Physica Polonica A
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2008
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vol. 114
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issue 3
637-647
EN
Two different, working examples of organization of econophysics graduate courses at the Faculty of Physics, University of Warsaw and the Department of Physics and Astronomy of the Wrocław University are considered. In the first example we have a system where the interdisciplinary, econophysical education begins only after three years study of physics. Within this system the M.Sc. as well as Ph.D. theses in econophysics are conducted only at the Faculty of Physics. In the second example the B.Sc. theses in econophysics are accomplished in the Department of Physics and Astronomy again after three years study but higher degrees can be prepared either in physics in the Institute of Theoretical Physics or in economy in the Institute of Economical Sciences. M.Sc. and Ph.D. theses can also be conducted. For both examples, the graduate students of econophysics are obliged to participate in traditional (typical) economical lectures and trainings which are offered them by economical departments while lectures and trainings (tutorials and/or laboratory classes) in econophysics are offered them by physics departments themselves. Thus Poland is one of a few countries, where so modern interdisciplinary knowledge is systematically offered to students.
3
Content available remote

Multifractal Background Noise of Monofractal Signals

100%
Grech D., Pamuła G.
Acta Physica Polonica A
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2012
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vol. 121
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issue 2B
B-34-B-39
EN
We investigate the presence of multifractal residual background effect for monofractal signals which appears due to the finite length of the signals and (or) due to the constant long memory the signals reveal. This phenomenon is investigated numerically within the multifractal detrended fluctuation analysis (MF-DFA) for artificially generated time series. Next, the analytical formulas enabling to describe the multifractal content in such signals are provided. Final results are shown in the frequently used generalized Hurst exponent h(q) multifractal scenario as a function of time series length L and the autocorrelation scaling exponent value γ. The obtained results may be significant in any practical application of multifractality, including financial data analysis, because the "true" multifractal effect should be clearly separated from the so called "multifractal noise" resulting from the finite data length. Examples from finance in this context are given. The provided formulas may help to decide whether one deals with the signal of real multifractal origin or not and make further step in analysis of the so called spurious or corrupted multifractality discussed in literature.
4
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Multifractal Dynamics of Stock Markets

100%
Czarnecki Ł., Grech D.
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issue 4
623-629
EN
We present a comparative analysis of multifractal properties of financial time series built on stock indices from developing (WIG) and developed (S&P500) financial markets. It is shown how the multifractal image of the market is altered with the change of the length of time series and with the economic situation on the market. We emphasize that the proper adjustment of scaling range for multiscaling power laws is essential to obtain the multifractal image of time series. We analyze in this paper multifractal properties of real financial time series using Hölder f(α) representation and multifractal-detrended fluctuation analysis method. It is also investigated how multifractal properties of stocks change with variety of "surgeries" done on the initial real financial time series. This way we reveal main phenomena on the market influencing its multifractal dynamics. In particular, we focus on examining how multifractal picture of real time series changes when one cuts off extreme events like crashes or rupture points, and how fluctuations around the main trend in time series influence the multifractal behavior of financial series in the long-time horizon for both developed and developing markets.
5
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Impact of Scaling Range on the Effectiveness of Detrending Methods

100%
Grech D., Mazur Z.
|
EN
We make the comparative study of scaling range properties for detrended fluctuation analysis (DFA), detrended moving average analysis (DMA) and recently proposed new technique called modified detrended moving average analysis (MDMA). Basic properties of scaling ranges for these techniques are reviewed. The efficiency and exactness of all three methods towards proper determination of scaling Hurst exponent H is discussed, particularly for short series of uncorrelated and persistent data.
6
Content available remote

Multifractality of Nonlinear Transformations with Application in Finances

100%
Grech D., Pamuła G.
Acta Physica Polonica A
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2013
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vol. 123
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issue 3
529-537
EN
We study the multifractal effects of nonlinear transformations of monofractal, stationary time series and apply the found results to measure the "true" unbiased multifractality generated only by multiscaling properties of initial (primary) data before transformations. A difference is stressed between "naive" observed multifractal effects calculated directly within detrended multifractal analysis as the spread Δh of the generalized Hurst exponents h(q) and the more reliable unbiased multifractality received after subtraction of residual bias effects generated by nonlinear transformations of initial data and coupled with finite size effects in time series. This property is investigated for volatile series of the real main world financial indices. A difference between multifractal properties of intraday and interday quotes is also pointed out in this context for the Warsaw Stock Exchange WIG index. Finally, based on the observed feature of real nonstationary data, a new measure of unbiased multifractality in signals is introduced. This measure comes from an analysis of the whole generalized Hurst exponent profile instead of looking just at its edge behavior h^{±} ≡ h(q→ ±∞). Such an approach seems to be particularly useful when h(q) is not a monotonic function of the moment order q. Interesting examples with extreme events from finance are presented. They convince that an analysis directed only on investigation of the edges h^{±} in multifractal spectrum may be misleading.
7
Content available remote

Methods of Non-Extensive Statistical Physics in Analysis of Price Returns on Polish Stock Market

81%
Bil Ł., Grech D., Podhajska E.
Acta Physica Polonica A
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2016
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vol. 129
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issue 5
986-992
EN
We use methods of non-extensive statistical physics to describe quantitatively the memory effect involved in returns of companies from WIG 30 index on the Warsaw Stock Exchange. The entropic approach based on the generalization of the Boltzmann-Gibbs entropy to non-additive Tsallis q-entropy is applied to fit fat tailed distribution of returns to q-normal (Tsallis) distribution. The existence of long term memory effects in price returns generated by two-point autocorrelations are checked via calculation of the Hurst exponent within detrended fluctuation analysis approach. The results are collected for diversified frequency of data sampling. We confirm the perfect inverse cubic power law for low time-lags (≈1 min) of returns for the main WIG 30 index as well as for the most of separate stocks, however this relationship does not hold for longer time-lags. The particular emphasis is given to a study of an independent fit of probability distribution of positive and negative returns to q-normal distribution. We discuss in this context the asymmetry between tails in terms of the Tsallis parameters q^{±}. A qualitative and quantitative relationship between the frequency of data sampling, the parameters q and q^{±}, and the corresponding main Hurst exponent H is provided to analyze the effect of memory in data caused by linear and nonlinear autocorrelations. A new quantifier based on asymmetry of the Tsallis index instead of skewness of distribution is proposed which we believe is able to describe the stage of market development and its robustness to speculation.
8
Content available remote

On the Zipf Strategy for Short-Term Investments in WIG20 Futures

81%
Bieda B., Chodorowski P., Grech D.
Acta Physica Polonica A
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2012
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vol. 121
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issue 2B
B-7-B-10
EN
We apply the Zipf power law to financial time series of WIG20 index daily changes (open-close values). Thanks to the mapping of time series signal into the sequence of 2k+1 'spin-like' states, where k=0, 1/2, 1, 3/2, ..., we are able to describe any time series increments, with almost arbitrary accuracy, as the one of such 'spin-like' states. This procedure leads in the simplest non-trivial case (k = 1/2) to the binary data projection. More sophisticated projections are also possible and mentioned in the article. The introduced formalism allows then to use Zipf power law to describe the intrinsic structure of time series. The fast algorithm for this implementation was constructed by us within Matlab^{TM} software. The method, called Zipf strategy, is then applied in the simplest case k = 1/2 to WIG 20 open and close daily data to make short-term predictions for forthcoming index changes. The results of forecast effectiveness are presented with respect to different time window sizes and partition divisions (word lengths in Zipf language). Finally, the various investment strategies improving return of investment (ROI) for WIG20 futures are proposed. We show that the Zipf strategy is the appropriate and very effective tool to make short-term predictions and therefore, to evaluate short-term investments on the basis of historical stock index data. Our findings support also the existence of long memory in financial data, exceeding the known in the literature 3 days span limit.
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