Negative values from High Pass filtering I come from Fluid Mechanics domain so pardon me for asking a naive and fundamental question. 

I am trying to perform high pass filtering on a set of positive real numbers (~Energy) using FFT. However, the result I obtain has a lot of negative values. I tried to quantify how many of them are negative and it seems $\sim50\%$ of these values are negative. 

I tried looking up for an answer and I saw a general approach used in Image processing domain, where people offset these negative values or use some threshold. But in my case, I can't use either of these techniques because I need to look at some statistical quantities after the filtering process. 

So I want to ask why do these negative numbers appear for a purely positive input and if so, are there any solutions for it?
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.