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I am writing a thesis and I simply want to check inference concerning my regressions. I have the following three questions:

1)
Some of the regressions exhibit autocorrelation, but since I only care about inference I wonder if I should try to fix any of the autocorrelation using first differences and ARMA models or not. If I will be fixing only some of these regressions (not all of them are autocorrelated) and I wish to compare one regressions's statistical significance of coefficients to those of another regression, won't it this be a case of comparing non-similar regressions (for example one of fisrt differences with another that has not been corrected in such a way) so I shouldn't try this at all (again I only care about inference)?

2)
Also, in the end if I indeed do not correct autocorrelation, I apply the following procedure to remove heteroscedasticity:

I check if a regression is heteroscedastic but not autoreggressive. If it only heteroscedastic, I apply the White correction for S.E.
If a regression is both heteroscedastic and autoreggressive, I apply the Newey-West correction for both.
If a regression is autoregressive but not heteroscedastic, I make no correction.

Is the above reasoning correct?

3)
I have variables with values that are way to large, so I thought to use logs (natural logarithms). The problem is that many of the values are negative. Does it make sense to first have the absolute values of the initial values, then log these only positive values and then multiply these loged values with the initial signs for each observations, so that in the end I keep the sign and have values loged?

I hope I am not non-senical about anything bera with me I'm only a student.

Thank you in advance for your concern.

I am writing a thesis and I simply want to check inference concerning my regressions. I have the following three questions:

1)
Some of the regressions exhibit autocorrelation, but since I only care about inference I wonder if I should try to fix any of the autocorrelation using first differences and ARMA models or not. If I will be fixing only some of these regressions (not all of them are autocorrelated) and I wish to compare one regressions's statistical significance of coefficients to those of another regression, won't it this be a case of comparing non-similar regressions (for example one of fisrt differences with another that has not been corrected in such a way) so I shouldn't try this at all (again I only care about inference)?

If a regression has autocorrelation and you ignore it, then the statistical inference is wrong. The correct comparisons have to be between estimates that both have correct inference. The usual first way to correct for serial correlation is either to include AR(1) in the regression or to use Newey-West standard errors.

3)
I have variables with values that are way to large, so I thought to use logs (natural logarithms). The problem is that many of the values are negative. Does it make sense to first have the absolute values of the initial values, then log these only positive values and then multiply these loged values with the initial signs for each observations, so that in the end I keep the sign and have values loged?

Why do you think your variables are "too large." All that should do is scale the regression coefficients. If you want to use logs as you suggest, make a graph of your transformed variable against X (just roughly) and see if you think you have a sensible functional form.

If a regression has autocorrelation and you ignore it, then the statistical inference is wrong. The correct comparisons have to be between estimates that both have correct inference. The usual first way to correct for serial correlation is either to include AR(1) in the regression or to use Newey-West standard errors.

Ok then since I only care about standard errors I will use Newey-west I just thought this is the proper test to use when both heteroscedasticity and autocorrelation are present (and this is what I was practically asking in question 2. One more question concerning this. I run the following code:

freeze(tab!j!i) B_Q!j_!i_ALL.auto(2, c) c(1)=0
if @val(tab!j!i(4,2))>@qchisq(.95,5)

which tests for an order 2 autocorrelation (as default) and if the Obs*rsquared value of this lm test surpasses the critical value of @qchisq(.95,5), then I run the Newey-west correction for this equation. Do you think this is enough? It will be too much problem for me to test all of my regressions for the correct AR(MA) model and I'm still afraid of mispecification anyway.

Why do you think your variables are "too large." All that should do is scale the regression coefficients. If you want to use logs as you suggest, make a graph of your transformed variable against X (just roughly) and see if you think you have a sensible functional form.

I'm sorry I wasn't explicit enough about this. I run regressions where one variable has very small values (number of buys or sells, positive -negative of a stock by insiders for a year), while the other one represents value in dollars of these trades (both positive and negative - large values), so my regressions have very small coefficients and very large standard errors. I don't know if the rsquared is affected this way as well. So I need to use logs for the large variable (I have graphed the two series together and it doesn't look sensible enough as you suggest). So is the transformation I have suggested reasonable enough anyway?

Thank you so much for your help