hac function: pvalues or confidence intervals

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

Answer 1

[Hang Qian]

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]

[Tamas Bodai]

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.

Answer 2

[Karoline Bax]

Hello,

that is great help! Thank you, is there a way to get the R-squared and adjusted R-squared too?