# Huge t-statistic vs Hetero. and Auto.

#### Akavall

##### New Member
Lets say I am working with time-series and I regressed y on x and I get a huge t-statistic, lets say 15. Would it be reasonable to assume that even if there is heteroskedasticity and autocorrelation, the relationship between x and y is still statistically significant because t-statistic is so huge. I've seen this done boeore, so I doubt it is wrong (totally wrong), but this looks strange. Any thoughts on this?

#### mp83

##### TS Contributor
When aytoCorr or heteroSc is present then standard errors are poorly estimated. Then you have to estimate them using a robust estimate, i.e White etc. Those estimates will be larger than the initial and therefor reduce the the t-statistics.

So , no matter the hugeness (sic) of t you have to go through this procedure.

Hope it doesn't ruin your x-y relationship!

#### Akavall

##### New Member
When aytoCorr or heteroSc is present then standard errors are poorly estimated. Then you have to estimate them using a robust estimate, i.e White etc. Those estimates will be larger than the initial and therefor reduce the the t-statistics.

So , no matter the hugeness (sic) of t you have to go through this procedure.

Hope it doesn't ruin your x-y relationship!
Calculating robust standard errors actually increased my t-statistic to 23.5! The problem is that I get a Durbin-Watson of 0.146, which is of course to low, e.i. I have a bad autocorrelation problem. I wonder if t-statistic of 23.5 can make up for that.

If I put my variables in first differences, there is no more relationship, but then again first differencing often lead to the loss of information.

Thanks again.

#### mp83

##### TS Contributor
I don't get that. When using White or something like that the only thing that chenge is s.e (which get larger) and that the denominator og the T statistic.So provided that the estimete remains unchanged (which is the situation hear) the t should get smaller.

By the way, what's your R square?

#### Akavall

##### New Member
Actually my s.e. decreased when I calculated robust s.e.

My R-squated is 0.68

#### mp83

##### TS Contributor
I don't get it...

If you can describe exactly what you have done so far

#### Akavall

##### New Member
I have two time-series variables, both are in logs, say y and x. If I regress y on x whithout using robust standard erros my t-statistic is about 15, if I regress it with robust standard erros the t-statistic goes up to 23.5.

Btw, what's the formula for the white's standard errors? I googled around for it, but couldn't find it.

#### Akavall

##### New Member
I think those are the formula's stata uses:

OLS variance estimator:
VOLS = s2 * (X'X)^-1

where
N
s2 = (1/(N - k)) Σ ei^2
i=1

Robust (unclustered) variance estimator:
N
Vrob = (X'X)^-1 * [ Σ (ei*xi)' * (ei*xi) ] * (X'X)^-1
i=1

http://www.stata.com/support/faqs/stat/cluster.html

I guess in my case
N
s2 = (1/(N - k)) Σ ei^2
i=1

is greater than

N
[ Σ (ei*xi)' * (ei*xi) ] * (X'X)^-1
i=1

#### Akavall

##### New Member
Thanks, this looks quite interesting.