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Similar to Juan Gil's answer but a bit differently I would say the following based on this: The OU process $$dX_t = \kappa(\theta-X_t)dt + \sigma dW_t$$ can be (Euler-Maryuama discretization) discretized at times $n \Delta t,n=1,\ldots,\infty $ which gives with $t = k \Delta t$ $$ X_{k+1} - X_k = \kappa \theta \Delta t -\kappa X_k \Delta t + \sigma (W_{k+1} ...


For a Ornstein-Uhlenbeck process, the maximum likelihood parameters are the ones from least squares regression. If your process is: $$ dX=\kappa (\theta-X)dt+\sigma dW $$ you can do a linear regression in the form $$ \frac{dX}{dt}=a+bX+\epsilon $$ So your parameters will be: $$ \kappa=-b $$ $$ \theta=-\frac{a}{b} $$ $$ \sigma=std(\epsilon dt) $$

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