# Brownian motion from price-series, what is the time step?

If I assume a given empirical price-series is a brownian motion, I can estimate the drift and standard deviation as long as I know what the time step was when the process was 'generated'.

But since this is an empirical price-series, how can I know what dt is supposed to be?

• What is the frequency of your empirical price data? If you are using daily data then $\Delta t$ is one day (i.e. 0.0039 years), for monthly data it is 1/12= 0.083 years, etc. – noob2 May 22 at 11:29
• @noob2 It's minute data. So are you saying t is in units of years, regardless of the frequency of the price-series? – wildbunny May 22 at 11:59
• (1) With minute data you have to be careful, there can be "micro-structure" phenomena like bid ask bounce which you might want to filter out before fitting a brownian motion (2) Year is the unit I like to use (for use with options), but you can use another unit more appropriate to what you are trying to do. – noob2 May 22 at 12:45