What is the real HIV window period?

I received training from the Department of Health in my state to do HIV education and testing. I was told that it usually only takes 3-4 months for antibodies to show up in a test, but in very rare cases, it can take up to 6 months for the antibodies to show up. Recommendation of testing 3 months post exposure and 6 months post exposure seems to be most common, and most reliable.