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I have two questions regarding the efficiency gain using GARCH modeling campared to OLS with HAC standard errors.

  1. If we compare the coefficient estimates from a regression using OLS and that from the same equation using GARCH modeling. They sometimes differ substaintially. Why is this the case?

  2. For serially correlated data, we can either use HAC standard errors (if we estimate the equation by OLS) or use GARCH modeling which gives the condtional mean and variance at the same time. Then the standard errors for the coefficients in the condtional mean equation will be derived from the conditional variance equation. What exactly is the efficiency gain if we directly estimate the GARCH model? (I only know that HAC has some prolem if the sample size is small..)

  3. If the results from the conditional mean equation in the GARCH model and the results from (the same equation) estimated by OLS with HAC standard errors differ should one always prefer the conditional mean equation from the GARCH model?

Looking forward for discussions!

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  1. Why would you generally expect identical or similar results from two different models? There may be special cases where the results are similar, but as long as the models differ, the results might also differ.
  2. To deal with serially correlated model errors you may either
    (a) model the serial correlation explicitly, e.g. by allowing the errors to follow an ARMA (or even ARMA-GARCH) process; or
    (b) by using HAC standard errors (which is also sometimes called White-washing to stress that HAC does not entirely solve the problem -- see e.g. Diebold "The HAC Emperor has no Clothes" and "The HAC Emperor has no Clothes: Part 2").
    The efficiency gain will depend on the application, but you can always try both (a) and (b) and see how much precision you gain from (a) over (b) in terms of the estimated standard errors of the model coefficients.
  3. If the GARCH model appears appropriate (passes the diagnostic tests and is justifiable from the subject-matter point of view), then why waste power with using HAC in place of GARCH. But it might not always be easy to come up with an appropriate model, and HAC is the easier solution (easiness being a merit in itself).
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