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Dynamics of the Number of Trades of Financial Securities

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Abstract

We perform a parallel analysis of the spectral density of (i) the logarithm of price and (ii) the daily number of trades of a set of stocks traded in the New York Stock Exchange. The stocks are selected to be representative of a wide range of stock capitalization. The observed spectral densities show a different power-law behavior. We confirm the $1/f^2$ behavior for the spectral density of the logarithm of stock price whereas we detect a $1/f$-like behavior for the spectral density of the daily number of trades.

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