Dynamics of the Number of Trades of Financial Securities

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 $1\mathrm{/}{f}^2$ behavior for the spectral density of the logarithm of stock price whereas we detect a $1\mathrm{/}f$-like behavior for the spectral density of the daily number of trades.