hac function: pvalues or confidence intervals

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Fregior on 18 Mar 2017
Commented: Tamas Bodai on 28 Apr 2021
Hi, the function
returns as coefficients the same of standard OLS. Is this correct? What changes is the covariance matrix.
At this point I would like to ask you how I could obtain the pvalues of the coefficients with hac methodology or how to get a confidence interval. I googled a bit but I could not find specific answer.

Accepted Answer

Hang Qian
Hang Qian on 28 Jun 2017
Hi Fregior,
Yes, the point estimator returned by HAC is the same as the OLS estimator.
HAC returns the covariance matrix EstCov. Then we can compute the standard erros, t-statistics, p-values and confidence intervals:
SE = sqrt(diag(EstCov))
tStat = OLS ./ SE
pVal = erfc(0.7071 * abs(tStat))
CI = [OLS-2*SE, OLS+2*SE]
  1 Comment
Tamas Bodai
Tamas Bodai on 28 Apr 2021
Dear Hang,
You seem to assume normality of the t-statistic. I wonder what is the correct formula for finite sample. In particular, what is the correct degree of freedom for the t-distribution that the t-statistic obeys? In the function ‘predict’, the t-distribution is used. Actually, I asked this question here. The function ‘hac’ does not seem to recalculate DFE. However, my intuition is that with some autocorrelation present, we have a smaller effective sample size and so degree of freedom. The printout by hac gives me the same effective sample size as the actual sample size, even if I apply it to data featuring autocorrelation. I wonder why the printout of this particular piece of information if it never changes.
Your help would be greatly appreciated.

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More Answers (1)

Karoline Bax
Karoline Bax on 2 Aug 2018
that is great help! Thank you, is there a way to get the R-squared and adjusted R-squared too?


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