@StephanKolassa A feedback mechanism? Because I'm interested in improving performance of regression on small datasets :) OLS is my starting point

@PeterFlom The idea is, that the values of the coefficients estimated by resampling aren't equal to coefficients estimated by MLE on that set of data. This leads to belief that the small sample size affects the MLE coefficients and the true coefficients are closer to the ones infered with resampling - but closer doesn't mean equal, which is why I thought about going bayesian.

@PeterFlom Yeah and the question is whether this information can be treated as a prior

@RichardHardy it's relevant because it was my suggestion about what to try. How exactly do you want to want to fit an AR(1) model to nonstationary data?

@RichardHardy yes, but I did in my first comment.

@RichardHardy auto-arima adjusts for stationarity by itself, so what is exactly the problem?

Honestly, this time series just doesn't seem to be autocorrelated. Try auto-arima with the seasonal component on, but I don't think it's gonna be easy to model this dataset

If so, then I can still do inference treating them separately I suppose. The question is, whether this approach is correct, or TLM are estimated in a different way? The link you've attached is too general for me, I'm not sure what exactly you want me to research.

For simplicity I assume the threshold to be known. I'm not sure I understand your second question, the regression function would be continuous since for one regime condition is "greater than" and the other "lesser or equal than". While dealing with possible threshold we are dealing with nonlinear regression - so threshold should decrease pot. heteroskedasticity as I see it

Thank you, I wouldn't think about it by myself! If you find a moment, please add it to your answer so the future generations can see it too :D

Oh I didn't know that! So the results with AIC and BIC will more or less converge in small datasets?

Because AIC - as far as I know but I might be wrong here - tends to choose more complex models than BIC, which is what I find prone to overfitting

I think what you are interested in is data leakage: towardsdatascience.com/…

Wouldn't AIC lead to overfitting in data-limited situation?