The discrete analogue of an OU process is a simple AR(1) model. More general AR(p) or ARMA(p,q) models can also be regarded as discrete analogues of an OU process? If so, which coefficients describe its mean-reverting behavior?
My assumption is that for AR(p) model, sum of all coefficients should capture the mean-reversion behavior of the process. If so, is this true for ARMA as well or mean-reversion pattern is also governed by MA coefficients?
Yes, you're correct.
In an AR(p) model, the sum of all autoregressive coefficients governs the mean-reverting behaviour in case of an OU process.
In an ARMA(p,q) model, the AR terms predominantly dictate the mean revertive behaviour, but the MA terms influence the path taken for the mean reversion.
An intuition would be to realize that the MA terms affect the short term behavior, but not the long term behavior of the process.
Reference: https://www.cs.upc.edu/~argimiro/mypapers/Journals/2014/ACCOUp2014.pdf (Page 12)
