arXiv subjects

R. Rak

Publications and source records attributed to R. Rak.

7 recordsLinked to original sources

arXiv2008

Different fractal properties of positive and negative returns

We perform an analysis of fractal properties of the positive and the negative changes of the German DAX30 index separately using Multifractal Detrended Fluctuation Analysis (MFDFA). By calculating the singularity spectra $f(α)$ we show that returns of both signs reveal multiscaling. Curiously, these spectra display a significant difference in the scaling properties of returns with opposite sign. The negative price changes are ruled by stronger temporal correlations than the positive ones, what is manifested by larger values of the corresponding Hölder exponents. As regards the properties of dominant trends, a bear market is more persistent than the bull market irrespective of the sign of fluctuations.

q-fin.ST↗

arXiv2008

Cross-correlations in Warsaw Stock Exchange

We study the inter-stock correlations for the largest companies listed on Warsaw Stock Exchange and included in the WIG20 index. Our results from the correlation matrix analysis indicate that the Polish stock market can be well described by a one factor model. We also show that the stock-stock correlations tend to increase with the time scale of returns and they approach a saturation level for the time scales of at least 200 min, i.e. an order of magnitude longer than in the case of some developed markets. We also show that the strength of correlations among the stocks crucially depends on their capitalization. These results combined with our earlier findings together suggest that now the Polish stock market situates itself somewhere between an emerging market phase and a mature market phase.

q-fin.ST↗

arXiv2007

Stock market return distributions: from past to present

We show that recent stock market fluctuations are characterized by the cumulative distributions whose tails on short, minute time scales exhibit power scaling with the scaling index alpha > 3 and this index tends to increase quickly with decreasing sampling frequency. Our study is based on high-frequency recordings of the S&P500, DAX and WIG20 indices over the interval May 2004 - May 2006. Our findings suggest that dynamics of the contemporary market may differ from the one observed in the past. This effect indicates a constantly increasing efficiency of world markets.

q-fin.ST↗

arXiv2006

Correlation matrix decomposition of WIG20 intraday fluctuations

Using the correlation matrix formalism we study the temporal aspects of the Warsaw Stock Market evolution as represented by the WIG20 index. The high frequency (1 min) WIG20 recordings over the time period between January 2001 and October 2005 are used. The entries of the correlation matrix considered here connect different distinct periods of the stock market dynamics, like days or weeks. Such a methodology allows to decompose the price fluctuations into the orthogonal eigensignals that quantify different modes of the underlying dynamics. The magnitudes of the corresponding eigenvalues reflect the strengths of such modes. One observation made in this paper is that strength of the daily trend in the WIG20 dynamics systematically decreases when going from 2001 to 2005. Another is that large events in the return fluctuations are primarily associated with a few most collective eigensignals.

physics.data-an↗

arXiv2006

Nonextensive statistical features of the Polish stock market fluctuations

The statistics of return distributions on various time scales constitutes one of the most informative characteristics of the financial dynamics. Here we present a systematic study of such characteristics for the Polish stock market index WIG20 over the period 04.01.1999 - 31.10.2005 for the time lags ranging from one minute up to one hour. This market is commonly classified as emerging. Still on the shortest time scales studied we find that the tails of the return distributions are consistent with the inverse cubic power-law, as identified previously for majority of the mature markets. Within the time scales studied a quick and considerable departure from this law towards a Gaussian can however be traced. Interestingly, all the forms of the distributions observed can be comprised by the single $q$-Gaussians which provide a satisfactory and at the same time compact representation of the distribution of return fluctuations over all magnitudes of their variation. The corresponding nonextensivity parameter $q$ is found to systematically decrease when increasing the time scales.

physics.data-an↗

arXiv2006

Multifractal Model of Asset Returns versus real stock market dynamics

There is more and more empirical evidence that multifractality constitutes another and perhaps the most significant financial stylized fact. A realistic model of the financial dynamics should therefore incorporate this effect. The most promising in this respect is the Multifractal Model of Asset Returns (MMAR) introduced by Mandelbrot in which multifractality is carried by time deformation. In our study we focus on the Lux extension to MMAR and empirical data from Warsaw Stock Exchange. We show that this model is able to reproduce relevant aspects of the real stock market dynamics.

physics.soc-ph↗

arXiv2005

Detecting subtle effects of persistence in the stock market dynamics

The conventional formal tool to detect effects of the financial persistence is in terms of the Hurst exponent. A typical corresponding result is that its value comes out close to 0.5, as characteristic for geometric Brownian motion, with at most small departures from this value in either direction depending on the market and on the time scales involved. We study the high frequency price changes on the American and on the German stock markets. For both corresponding indices, the Dow Jones and the DAX respectively, the Hurst exponent analysis results in values close to 0.5. However, by decomposing the market dynamics into pairs of steps such that an elementary move up (down) is followed by another move up (down) and explicitly counting the resulting conditional probabilities we find values typically close to 60%. This effect of persistence is particularly visible on the short time scales ranging from 1 up to 3 minutes, decreasing gradually to 50% and even significantly below this value on the larger time scales. We also detect some asymmetry in persistence related to the moves up and down, respectively. This indicates a subtle nature of the financial persistence whose characteristics escape detection within the conventional Hurst exponent formalism.

physics.soc-ph↗