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Feb 28 at 5:03 comment added RoninAmibo Indeed, I'm referring to exactly that.
Feb 28 at 0:27 comment added Dan Boschen @RoninAmibo no problem, was fun to investigate. As I mentioned in the comments, consider modeling as a leaky integrator of AWGN: y[n] = x[n] + beta y[n-1]. The closer beta is to 1 (but always less than 1!), the higher tau where it transitions from random walk. Maybe that is the same thing you are saying.
Feb 28 at 0:00 comment added RoninAmibo Hi @Dan, thank you very much for your help, your insights and you time. It is really appreciated. I'll therefore choose to model with an AR process (discrete version of the OU model) of order 1, with a coefficient really close to 1 so that it has a random walk behavior in low taus. The model will be compared with the dataset using the same tools as above. Thank you very, very much.
Feb 27 at 23:30 vote accept RoninAmibo
Feb 27 at 15:38 history edited Dan Boschen CC BY-SA 4.0
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Feb 16 at 22:38 history answered Dan Boschen CC BY-SA 4.0