# how to estimate Geometric Brownian Motion parameters on long timeseries [closed]

I'm working on a 50-years financial timeseries and I would like to simulate GBM paths from it. The first thing I'm supposed to do is to estimate the drift $$\mu$$ and the volatility $$\sigma$$ parameters.

What I've done so far is to come up with the estimate on the entire history, but I think it's quite a big approximation since the expected return and the volatility of a financial asset vary over time. Also, it is known that GBM doesn't work so well on long time interval.

I thought that I could have time-dependent deterministic parameters for $$\mu = \mu(t)$$ and $$\sigma = \sigma(t)$$ where I compute the values for every years and update the parameters of the GBM accordingly, but I'm not sure if it makes sense.

Any suggestion?