# Ornstein versus AR(1) for modeling stationary data

I've come across several posts regarding parameter estimation for O-U models given some stationary data (say, some sort of mean reverting spread), but I can't seem to find an answer as to why modeling the data as a continuous O-U bears a benefit over modeling it as an AR(1) process. Are the parameters more robust/precise when treating the process as O-U versus AR(1)? I suppose O-U may give better estimates at higher frequencies. Any insight would be great.

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EDIT: You can see AR(1) below $$x_{k+1} = c + a x_k + b\varepsilon_k$$ and by substituting c=θμΔt, a=−θΔt and $b = \sigma\sqrt{\Delta t} \space$ you will get OU $$x_{k+1} = \theta(\mu - x_k)\Delta t + \sigma \varepsilon_k\sqrt{\Delta t}$$