Spurious trend switching phenomena in financial markets

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Abstract

The observations of power laws in the time to extrema of volatility, volume and intertrade times, from milliseconds to years reported by Preis et al. (2010, 2011), are shown to result straightforwardly from the selection of biased statistical subsets of realizations in otherwise featureless processes such as random walks. The bias stems from the selection of price peaks that imposes a condition on the statistics of price change and of trade volumes that skew their distributions. For the intertrade times, the extrema and power laws results from the format of transaction data.