Physicists have rebuffed the existence of power laws governing the dynamics of traded stock volatility, volume and intertrade times at times of stock price extrema. They did this by demonstrating that what appeared as "switching points" in financial markets trends was due to a bias in the interpretation of market data statistics. This study by Vladimir Filimonov and Didier Sornette from the Department of Management, Technology and Economics at ETH Zurich in Switzerland is about to be published in EPJ B¹.
The authors noticed that increasing misinterpretations of market dynamic stemmed from statistical analysis of conditional probability: the probability that an event will occur, subject to a prior event occuring. A previous study based on such statistics suggested that the local maxima of volatility and volume, and local minima of intertrade times are akin to switching points in financial returns, reminiscent of critical transition points in physics between two phases, e.g. liquid and gas. These local extrema were thought to follow approximate power laws in time scales ranging from milliseconds to years.
To disentangle the effect of the conditional statistics on the market data trends, the authors compared stock prices traded on the financial market with a known statistical model of price featuring simple random behaviour, called Geometrical Brownian Motion (GBM). They demonstrated that "switching points" occur in the GBM model, too.
The authors found that, in the case of volatility data, the misguided interpretation of switching points stems from a bias in the selection of price peaks that imposes a condition on the statistics of price change, skewing its distributions. Under this bias, switching points in volume appear naturally due to the volume-volatility correlation. For the intertrade times, they showed that extrema and power laws result from the bias introduced in the format of transaction data.
References:
1. Filimonov V., Sornette D. (2012), Spurious trend switching phenomena in financial markets, European Physical Journal B (EPJ B) DOI 10.1140/epjb/e2012-21060-1
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Journal
The European Physical Journal B