For the record, then, let's point out that the two basic approaches to heteroskedasticity in gretl -- namely, switching to "robust" standard errors, or switching from OLS to GLS via the "hsk" command -- do not require taking logs of negative numbers. The following script illustrates. The series y and x contain both positive and negative values, and the data-generating process is heteroskedastic by construction.

<hansl>
nulldata 50
set seed 3711
series x = normal()
# generate heteroskedastic y
series y = -1 + 3*x + normal()*x
# verify we have negative values in both y and x
print y x --byobs
# run OLS
ols y 0 x
# try robust standard errors: no problem
ols y 0 x --robust
# try GLS: again, no problem
hsk y 0 x
</hansl>

In this case the "hsk" command produces a closer approximation to the true x-slope of 3.0 (2.997, versus 3.098 from OLS), although obviously one would have to replicate the example a large number of times to verify that (as theory says) the hsk estimates are more efficient, given heteroskedasticity.

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