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O-U is continuous time mean reverting process, hence used to model stationary series. It has closed form analytic solution. This allows insight into stationary processes and act like asymptotic limiting case for calculating coefficients that matter.

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 $$ x_{k+1} = \theta(\mu - x_k)\Delta t + \sigma \varepsilon_k\sqrt{\Delta t}$$

This is simple discretization. Then multivariate OU model can be used for statistical arbitrage between a pair of assets that are cointegrated.

O-U is continuous time mean reverting process, hence used to model stationary series. It has closed form analytic solution. This allows insight into stationary processes and act like asymptotic limiting case for calculating coefficients that matter.

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 $$ x_{k+1} = \theta(\mu - x_k)\Delta t + \sigma \varepsilon_k\sqrt{\Delta t}$$

This is simple discretization to show they are same and how the parameters can be translated. O-U can be used to detect the steady state parameters. As you see paramaters are interchangeable, frequency used in AR and O-U should be same, then it will be frequency agnostic. I am doing some work on pair trading using O-U I will re-edit at some later time.

O-U is continuous time mean reverting process, hence used to model stationary series. It has closed form analytic solution. This allows insight into stationary processes and act like asymptotic limiting case for calculating coefficients that matter.

I think you want something like this from AR(1) below $$x_{k+1} = c + a x_k + b\varepsilon_k$$ and substitute c=θμΔt, a=−θΔt and $b = \sigma\sqrt{\Delta t} \space$ to get OU $$ x_{k+1} = \theta(\mu - x_k)\Delta t + \sigma \varepsilon_k\sqrt{\Delta t}$$

O-U is continuous time mean reverting process, hence used to model stationary series. It has closed form analytic solution. This allows insight into stationary processes and act like asymptotic limiting case for calculating coefficients that matter.

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 $$ x_{k+1} = \theta(\mu - x_k)\Delta t + \sigma \varepsilon_k\sqrt{\Delta t}$$

This is simple discretization. Then multivariate OU model can be used for statistical arbitrage between a pair of assets that are cointegrated.

O-U is continuous time mean reverting process, hence used to model stationary series. It has closed form analytic solution. This allows insight into stationary processes and act like asymptotic limiting case for calculating coefficients that matter.

O-U is continuous time mean reverting process, hence used to model stationary series. It has closed form analytic solution. This allows insight into stationary processes and act like asymptotic limiting case for calculating coefficients that matter.

I think you want something like this from AR(1) below $$x_{k+1} = c + a x_k + b\varepsilon_k$$ and substitute c=θμΔt, a=−θΔt and $b = \sigma\sqrt{\Delta t} \space$ to get OU $$ x_{k+1} = \theta(\mu - x_k)\Delta t + \sigma \varepsilon_k\sqrt{\Delta t}$$