Negative values from High Pass filtering
A high pass filter will remove a large portion to all of the 0 Hz component or DC offset from a signal.  That's similar to subtracting the mean average, which for a normally distributed signal will make around half of the signal negative (since it was below the original average mean).  

If you want the mean to be the same after a high pass filter, you could always add it back.

If you don't care about the actual mean value, you could also add an arbitrarily large positive offset to make sure the sum was always positive.