It sounds like cut-off or automation aren't what you think the are. Automation is (for standard DAWs) where you draw a line or curve that defines how some parameter changes over time. In this case filter cut-off, that is the frequency knob of the HP filter, is controlled by one of those curves. So your question doesn't really make sense. Automation can be for any parameter (depending on the DAW) over any time period and over any range of values (depending on the parameter).