Let's say I'm modeling the trading volume of a stock price (e.g. Apple Inc.) to follow a Geometric Brownian Motion and I want to estimate the parameters (i.e. drift and volatility) using historical data. I am assuming that a GBM matches the time series pretty well. If I was modeling a stock price itself, I would calculate the drift and volatility by looking at the returns. However, applying this to the trading volume does not seem right to me since the trading volume, unlike a stock price, does not have any returns and if I am not looking at the returns the time series is non-stationary.
Q: How would I calculate the drift and volatility of such a historical time series to calibrate my GBM?