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I would like to recover the parameters of a Ornstein-Uhlenbeck process from observations that are irregularly spaced. Estimation via linear regression and maximum likelihood is demonstrated here for the case where the observations arrive at regularly spaced intervals. What would be the solution for irregularly sampled data?

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I haven't done this myself, but my first instinct would be to see if we can express OU process as a state space model. These can be estimated on uneven intervals, missing data etc.

Here's the paper which estimates OU process with a Kalman filter.

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