Current log-periodic view on future world market development

Applicability of the concept of financial log-periodicity is discussed and encouragingly verified for various phases of the world stock markets development in the period 2000-2010. In particular, a speculative forecasting scenario designed in the end of 2004, that properly predicted the world stock market increases in 2007, is updated by setting some more precise constraints on the time of duration of the present long-term equity market bullish phase. A termination of this phase is evaluated to occur in around November 2009. In particular, on the way towards this dead-line, a Spring-Summer 2008 increase is expected. On the precious metals market a forthcoming critical time signal is detected at the turn of March/April 2008 which marks a tendency for at least a serious correction to begin. In the present extended version some predictions for the future oil price are incorporated. In particular a serious correction on this market is expected to start in the coming days.Comment: presented by S. Drozdz at FENS2007 conference, 10 pages, 6 Figs, an extended version with the oil market included (Fig.7

Detrended cross-correlations between returns, volatility, trading activity, and volume traded for the stock market companies

We consider a few quantities that characterize trading on a stock market in a fixed time interval: logarithmic returns, volatility, trading activity (i.e., the number of transactions), and volume traded. We search for the power-law cross-correlations among these quantities aggregated over different time units from 1 min to 10 min. Our study is based on empirical data from the American stock market consisting of tick-by-tick recordings of 31 stocks listed in Dow Jones Industrial Average during the years 2008-2011. Since all the considered quantities except the returns show strong daily patterns related to the variable trading activity in different parts of a day, which are the best evident in the autocorrelation function, we remove these patterns by detrending before we proceed further with our study. We apply the multifractal detrended cross-correlation analysis with sign preserving (MFCCA) and show that the strongest power-law cross-correlations exist between trading activity and volume traded, while the weakest ones exist (or even do not exist) between the returns and the remaining quantities. We also show that the strongest cross-correlations are carried by those parts of the signals that are characterized by large and medium variance. Our observation that the most convincing power-law cross-correlations occur between trading activity and volume traded reveals the existence of strong fractal-like coupling between these quantities

Criticality Characteristics of Current Oil Price Dynamics

Methodology that recently lead us to predict to an amazing accuracy the date (July 11, 2008) of reverse of the oil price up trend is briefly summarized and some further aspects of the related oil price dynamics elaborated. This methodology is based on the concept of discrete scale invariance whose finance-prediction-oriented variant involves such elements as log-periodic self-similarity, the universal preferred scaling factor lambda=2, and allows a phenomenon of the "super-bubble". From this perspective the present (as of August 22, 2008) violent - but still log-periodically decelerating - decrease of the oil prices is associated with the decay of such a "super- bubble" that has started developing about one year ago on top of the longer-term oil price increasing phase (normal bubble) whose ultimate termination is evaluated to occur in around mid 2010.Comment: to appear in Acta Physica Polonica

Wavelet-based discrimination of isolated singularities masquerading as multifractals in detrended fluctuation analyses

The robustness of two widespread multifractal analysis methods, one based on detrended fluctuation analysis and one on wavelet leaders, is discussed in the context of time-series containing non-uniform structures with only isolated singularities. Signals generated by simulated and experimentally-realized chaos generators, together with synthetic data addressing particular aspects, are taken into consideration. The results reveal essential limitations affecting the ability of both methods to correctly infer the non-multifractal nature of signals devoid of a cascade-like hierarchy of singularities. Namely, signals harboring only isolated singularities are found to artefactually give rise to broad multifractal spectra, resembling those expected in the presence of a well-developed underlying multifractal structure. Hence, there is a real risk of incorrectly inferring multifractality due to isolated singularities. The careful consideration of local scaling properties and the distribution of Hölder exponent obtained, for example, through wavelet analysis, is indispensable for rigorously assessing the presence or absence of multifractality.Fil: Oswiecimka, Pawel. Polish Academy of Sciences; ArgentinaFil: Drozdz, Stanislaw. Cracow University of Technology. Faculty of Materials Engineering and Physics; PoloniaFil: Frasca, Mattia. University of Catania. Department of Electrical Electronic and Computer Engineering; ItaliaFil: Gebarowski, Robert. Cracow University of Technology. Faculty of Materials Engineering and Physics; PoloniaFil: Yoshimura, Natsue. Tokyo Institute of Technology. Institute of Innovative Research. FIRST; JapónFil: Zunino, Luciano José. Universidad Nacional de La Plata. Facultad de Ingeniería. Departamento de Ciencias Básicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Centro de Investigaciones Ópticas. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Centro de Investigaciones Ópticas. Universidad Nacional de La Plata. Centro de Investigaciones Ópticas; ArgentinaFil: Minati, Ludovico. Universita degli Studi di Trento; Italia. Polish Academy of Sciences; Argentin

World stock market: more sizeable trend reversal likely in February/March 2010

Based on our "finance-prediction-oriented" methodology which involves such elements as log-periodic self-similarity, the universal preferred scaling factor lambda=2, and allows a phenomenon of the "super-bubble" we analyze the 2009 world stock market (here represented by the SP500, Hang Seng and WIG) development. We identify elements that indicate the third decade of September 2009 as a time limit for the present bull market phase which is thus to be followed by a significant correction. In this context we also interpret the Chinese stock market index SSE. The third decade of September 2009 was accompanied with a stock market correction typically within the range of 4-5% worldwide. Taking into account the market patterns that followed the time of delivering the previous scenario we present an updated scenario whose critical time corresponds to October 28, 2009. Assuming quite evident (as of November 12, 2009) termination of the correction due to the above critical time we extend - consistently with our methodology - the stock market forecasting scenario. The corresponding expected SP500 future trend is shown in Fig. 5 and it supports a potential average continuation of increases to as far into the future as the turn of February/March 2010. We also indicate the log-periodic patterns on the gold market and they point to the end of November 2009 as the time when the trend reversal - likely local however - is expected to begin.