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Suppose we estimate the regression model $$\triangle y_{t}=\alpha + \beta y_{t-1}+\varepsilon_{t}$$ This is actually quite similar to the Dickey-Fuller test. If $\beta=0$, then the process has a unit root. Let's proceed assuming that $\beta<0$, i.e. that the process is stationary. The first equation is also similar to the continuous time ...

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What you are saying might be correct for discrete time processes. In continuous time the process $$dX_t = X_t^2 dW_t,\quad X_0 > 0$$ is stationary but not mean reverting.

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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 $t = k \Delta t$ $$X_{k+1} - X_k = \kappa \theta \Delta t -\kappa X_k \Delta t + \sigma (W_{k+1} ... 2 For a Ornstein-Uhlenbeck process, the maximum likelihood parameters are the ones from least squares regression. If your process is:$$ 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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