Using Mathematica I took the Discrete Fourier Transform (DFT) of a vector whose entries are volumes of a particular stock. The power spectrum is plotted below:
There are two questions that I have about the taking the DFT of a stock's volume:
- What is the interpretation of this transform for volume?
- Do the spikes on the left and right hand sides of the graph correspond to the Gibbs phenomenon?
Here is a plot of the volume before being transformed via DFT:
I will answer 2), which is a mathematical question, and refer you to Quantitative Finance for part 1).
Since you are transforming a real-valued function, the frequency plot is symmetric. The line of symmetry corresponds to the Nyquist frequency which is one half of the sampling rate ($125$ in your case). This means that only the part from $0$ to $125$ needs to be considered; the rest is its mirror image.
The spike near $0$ is a consequence of the fact that you are transforming a very large positively-valued function. Indeed, the frequency of $0$ corresponds to the constant term in the Fourier expansion, which is simply the average of the volume. It does not tell you anything about the dynamics of the volume. To get a better picture, I would subtract the average of stock volume from the data before applying the Fourier transform.