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Do you know any derivations (or references) which quantify the biasedness of ML estimators of an AR(p) process?

Richard Hardy
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shani
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  • ML conditional on the first observations is equivalent to ordinary least squares, so the same results apply. You may be interested in this post and this. – javlacalle Oct 24 '18 at 22:08
  • ML not conditional on a fixed vector (usually zeros) for the initial observations: Searching for information about bias reduction and bootstrap in AR models, you may find papers that estimate the bias by simulations and probably give some derivation
    or reference for the expression of the bias. For example, in a quick search I found this paper.     – javlacalle Oct 24 '18 at 22:08
  • @javlacalle yes, conditional ML is equivalent to OLS. However, aren't they just used as initializations to obtain ML estimates? Is it reasonable to compare biasedness of OLS to MLE? – shani Oct 25 '18 at 06:57
  • Yes, it is reasonable to compare those biases but I don't have the expressions to be compared. I just mentioned the equivalence in the the case of conditional ML because it may be easier to analyse the bias in terms of the OLS estimator as shown in one of the linked posts. – javlacalle Oct 25 '18 at 13:20
  • I think I recall Hamilton's Time Series Analysis doing this, but I don't have a copy on hand. – John Madden Nov 20 '22 at 14:22

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