Time scales involved in market emergence

In addressing the question of the time scales characteristic for the market formation, we analyze high frequency tick-by-tick data from the NYSE and from the German market. By using returns on various time scales ranging from seconds or minutes up to two days, we compare magnitude of the largest eigenvalue of the correlation matrix for the same set of securities but for different time scales. For various sets of stocks of different capitalization (and the average trading frequency), we observe a significant elevation of the largest eigenvalue with increasing time scale. Our results from the correlation matrix study go in parallel with the so-called Epps effect. There is no unique explanation of this effect and it seems that many different factors play a role here. One of such factors is randomness in transaction moments for different stocks. Another interesting conclusion to be drawn from our results is that in the contemporary markets the emergence of significant correlations occurs on time scales much smaller than in the more distant history.Comment: 13 page

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.Comment: to appear in Physica

The LIL for canonical U-statistics of order 2

Let X,X_1,X_2,... be independent identically distributed random variables and let h(x,y)=h(y,x) be a measurable function of two variables. It is shown that the bounded law of the iterated logarithm, $\limsup_n (n\log\log n)^{-1}|\sum_{1<= i< j<= n}h(X_i,X_j)|<\infty$ a.s., holds if and only if the following three conditions are satisfied: h is canonical for the law of X (that is Eh(X,y)=0 for almost y) and there exists $C<\infty$ such that, both, $E\min(h^2(X_1,X_2),u)<C\log\log u$ for all large u and $sup\{Eh(X_1,X_2)f(X_1)g(X_2):|f(X)|_2<1,\|g(X)\|_2<1, \|f\|_\infty<\infty, \|g\|_\infty<\infty\}< C$.Comment: 36 page

Zmiany znaczeniowe wybranych czasowników mówienia zanikających w dobie nowopolskiej

The paper presents semantic changes to verbs of speech. These verbs are identified as obsolete in the lexicographical sources. The material was collected from Słownik języka polskiego, ed. W. Doroszewski, vol. 1–11, PAN, Warszawa 1958–1969 (reprint) and contains verbs qualified as: archaic, obsolete and getting out of use. 25 lexical units considered verbs of speech were analysed. These units have chronological and other qualifiers (e.g. dialectal, colloquial, humorous). Lexicographic data confirms the presence of various processes associated with the emergence of new and disappearance of unwanted meanings.Artykuł dotyczy zmian znaczeniowych wybranych czasowników mówienia, określonych w źródłach leksykograficznych jako nacechowane chronologicznie dawnością. Podstawę badawczą stanowią wyekscerpowane na podstawie Słownika języka polskiego, red. W. Doroszewski, t. 1–11, PAN, Warszawa 1958–1969 (reprint) czasowniki z kwalifikatorami dawne, przestarzałe, wychodzące z użycia. Analizie leksykograficznej zostało poddanych 25 jednostek leksykalnych uznanych za czasowniki mówienia, które oprócz kwalifikatorów chronologicznych miały także inne kwalifikatory wskazujące na jakieś ograniczenia związane z ich użyciem (np. gwarowe, potoczne, żartobliwe itp.). Informacje leksykograficzne potwierdzają istnienie różnorodnych procesów związanych z kształtowaniem się nowych i zanikaniem już niepotrzebnych znaczeń

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.Comment: 14 pages. Physica A in prin

Effect of detrending on multifractal characteristics

Different variants of MFDFA technique are applied in order to investigate various (artificial and real-world) time series. Our analysis shows that the calculated singularity spectra are very sensitive to the order of the detrending polynomial used within the MFDFA method. The relation between the width of the multifractal spectrum (as well as the Hurst exponent) and the order of the polynomial used in calculation is evident. Furthermore, type of this relation itself depends on the kind of analyzed signal. Therefore, such an analysis can give us some extra information about the correlative structure of the time series being studied.Comment: Presented by P. O\'swi\k{e}cimka at FENS2012 conference, 17 pages, 9 figure

Alternation of different fluctuation regimes in the stock market dynamics

Based on the tick-by-tick stock prices from the German and American stock markets, we study the statistical properties of the distribution of the individual stocks and the index returns in highly collective and noisy intervals of trading, separately. We show that periods characterized by the strong inter-stock couplings can be associated with the distributions of index fluctuations which reveal more pronounced tails than in the case of weaker couplings in the market. During periods of strong correlations in the German market these distributions can even reveal an apparent L\'evy-stable component.Comment: 19 page