0

What are the options for unbiased estimators of AR(1) (or AR(p)) models?

Bias reduction techniques may also be included (jack knife would be one). I found one paper called "Bias correction using the bootstrap methods", but other than that not many hits. We may additionally assume that the error term is normal, then I also wonder whether it would be possible to estimate the error directly analytically.

Note that the answer in the question "Unbiased estimator for AR(p) model" looks wrong. The book details some alternative procedure.

Richard Hardy
  • 54,375
  • 10
  • 95
  • 219
Tony
  • 303
  • 2
  • 11
  • unbiased estimator of what ? The AR(1) has a variance, one parameter and a possibly a non-zero mean. – mlofton Jun 20 '20 at 03:41
  • @miofton The coefficient parameter value. – Tony Jun 20 '20 at 04:06
  • Hi: That bootstrap paper is fairly recent ( the 2000's ). So, if they're bootstrapping there, I would seriously doubt that an analytical solution for the bias exists. Otherwise, the bootstrap paper wouldn't exist because you could create an unbiased estimator directly just by subtracting the analytically derived bias from the estimate. – mlofton Jun 20 '20 at 13:34
  • There are two answers in the linked thread. Which one do you think is wrong and how/why? *The book* -- what book? – Richard Hardy Jun 20 '20 at 19:24
  • @RichardHardy First answer does not address how to remove the bias, and the second answer referring to page 223 of Hamilton's Time Series Analysis is wrong, the procedure is not for removing bias of AR models. – Tony Jun 20 '20 at 21:42
  • @mlofton The formula for the bias term is $\sum E(\frac{\epsilon_iy_{i-1}}{\sum y_{i-1}^2})$, which seems computable although perhaps not very quickly. However, a lot faster in small samples... – Tony Jun 20 '20 at 21:57
  • @Tony: I don't have time to read the paper but I would check that carefully because if the bias can be calculated, I'm surprised they would publish a bootstrap paper ? You're summing an expectation so could it be that it's difficult to get an unbiased estimator of the expectation ? I'm sorry that I can't help more but to understand the paper would take me time that I don't have right now. Actually, it's also possible that I couldn't understand it even if I took the time !!!!!!! – mlofton Jun 20 '20 at 22:17

0 Answers0