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We highlight a very simple statistical tool for the analysis of financial bubbles, which has already been studied in [1]. We provide extensive empirical tests of this statistical tool and investigate analytically its link with stocks correlation structure.
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Multifractality is ubiquitously observed in complex natural and socioeconomic systems. Multifractal analysis provides powerful tools to understand the complex nonlinear nature of time series in diverse fields. Inspired by its striking analogy with hydrodynamic turbulence, from which the idea of multifractality originated, multifractal analysis of financial markets has bloomed, forming one of the main directions of econophysics. We review the multifractal analysis methods and multifractal models adopted in or invented for financial time series and their subtle properties, which are applicable to time series in other disciplines. We survey the cumulating evidence for the presence of multifractality in financial time series in different markets and at different time periods and discuss the sources of multifractality. The usefulness of multifractal analysis in quantifying market inefficiency, in supporting risk management and in developing other applications is presented. We finally discuss open problems and further directions of multifractal analysis.
The investor is interested in the expected return and he is also concerned about the risk and the uncertainty assumed by the investment. One of the most popular concepts used to measure the risk and the uncertainty is the variance and/or the standard-deviation. In this paper we explore the following issues: Is the standard-deviation a good measure of risk and uncertainty? What are the potentialities of the entropy in this context? Can entropy present some advantages as a measure of uncertainty and simultaneously verify some basic assumptions of the portfolio management theory, namely the effect of diversification?
An average instantaneous cross-correlation function is introduced to quantify the interaction of the financial market of a specific time. Based on the daily data of the American and Chinese stock markets, memory effect of the average instantaneous cross-correlations is investigated over different price return time intervals. Long-range time-correlations are revealed, and are found to persist up to a month-order magnitude of the price return time interval. Multifractal nature is investigated by a multifractal detrended fluctuation analysis.
The stock market has been known to form homogeneous stock groups with a higher correlation among different stocks according to common economic factors that influence individual stocks. We investigate the role of common economic factors in the market in the formation of stock networks, using the arbitrage pricing model reflecting essential properties of common economic factors. We find that the degree of consistency between real and model stock networks increases as additional common economic factors are incorporated into our model. Furthermore, we find that individual stocks with a large number of links to other stocks in a network are more highly correlated with common economic factors than those with a small number of links. This suggests that common economic factors in the stock market can be understood in terms of deterministic factors.
We define a financial bubble as a period of unsustainable growth, when the price of an asset increases ever more quickly, in a series of accelerating phases of corrections and rebounds. More technically, during a bubble phase, the price follows a faster-than-exponential power law growth process, often accompanied by log-periodic oscillations. This dynamic ends abruptly in a change of regime that may be a crash or a substantial correction. Because they leave such specific traces, bubbles may be recognised in advance, that is, before they burst. In this paper, we will explain the mechanism behind financial bubbles in an intuitive way. We will show how the log-periodic power law emerges spontaneously from the complex system that financial markets are, as a consequence of feedback mechanisms, hierarchical structure and specific trading dynamics and investment styles. We argue that the risk of a major correction, or even a crash, becomes substantial when a bubble develops towards maturity, and that it is therefore very important to find evidence of bubbles and to follow their development from as early a stage as possible. The tools that are explained in this paper actually serve that purpose. They are at the core of the Financial Crisis Observatory at the ETH Zurich, where tens of thousands of assets are monitored on a daily basis. This allow us to have a continuous overview of emerging bubbles in the global financial markets. The companion report available as part of the Notenstein white paper series (2014) with the title ``Financial bubbles: mechanism, diagnostic and state of the World (Feb. 2014) presents a practical application of the methodology outlines in this article and describes our view of the status concerning positive and negative bubbles in the financial markets, as of the end of January 2014.
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