hac function: pvalues or confidence intervals

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Fregior
Fregior 2017-3-18
评论： Tamas Bodai 2021-4-28
Hi, the function
hac
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.
Thanks

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Hang Qian
Hang Qian 2017-6-28
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]
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Tamas Bodai
Tamas Bodai 2021-4-28
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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Karoline Bax
Karoline Bax 2018-8-2
Hello,
that is great help! Thank you, is there a way to get the R-squared and adjusted R-squared too?

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