زمان و معیار تجزیه و تحلیل توان هرست برای بازارهای مالی

We use a new method of studying the Hurst exponent with time and scale dependency. This new approach allows us to recover the major events affecting worldwide markets (such as the September 11th terrorist attack) and analyze the way those effects propagate through the different scales. The time–scale dependence of the referred measures demonstrates the relevance of entropy measures in distinguishing the several characteristics of market indices: “effects” include early awareness, patterns of evolution as well as comparative behaviour distinctions in emergent/established markets.

The main goal of this study is the analysis of stock exchange world indices searching for signs of coherence and/or synchronization across the set of studied markets. We have expanded the scope of previous work on the PSI-20 (Portuguese Standard Index), since results there [7] seemed to provide a basis for a wider ranging study of coherence and entropy. With that purpose we applied econophysics techniques related to measures of “disorder”/complexity (entropy) and a newly proposed [8] generalisation of Detrended Fluctuation Analysis. As a measure of coherence among a selected set of markets we have studied the eigenvalues of the correlation matrices for two different set of markets [11], exploring the dichotomy represented by emerging and mature markets and proposing a more refined classification. The indices are used to represent or characterise the respective market. The classification of markets into mature or emergent is not a simple issue. The International Finance Corporation (IFC) uses per capita income and market capitalisation relative to Gross National Product (GNP) for classifying equity markets. If either (i) a market resides in a low or middle-income economy, or (ii) the ratio of the investable market capitalisation to GNP is low, then the IFC classifies the market as emerging, otherwise the classification is mature. The data used in this study was taken daily for a set of worldwide market indices. As is usual in this kind of analysis [5] we base our results on the study of log returns View the MathML sourceηi=logxixi−1, where ηiηi is the log return at time step ii.

We applied the TSH to study market evolution over time for a range of markets, variously classified as mature, emerging and hybrid, (with behaviour in the last category switching between the other two). TSH was used to compare the market set and to establish classes displaying similar behaviour at any given time. This classification allows us to distinguish major events that affect several markets, as opposed to local fluctuations in a single (or few) markets. Examples, reflected worldwide, include the Asian tiger crashes(1997), 9/11 in 2001 — cited above, the Madrid bomb attacks (2004), and others. The resulting classification is in agreement with that proposed by our wavelet analysis, proposed in Ref. [12].