I am planning to build a linear regression model where I explain flight ticket demand with airfares, lagged airfares, GDP etc. based on monthly data from the past 15 years. This is my first time working with time series and - if I got it right - some of my variables are trend-stationary. So my plan is to use a Hodrick-Prescott-Filter to take the trend out and just use the remaining, detrended data in my regression.
My question is: Does this change the interpretation of the results I get?
To clarify: I already took the natural logarithms of all my variables, so my regression model will look something like:
ln(ticketdemandt) = ß0 + ß1t * ln(pricet) + ß2t-k * ln(pricet-k) + ß3t * ln(GDPt) + ... + ut
(sorry about the confusing t and t-k, they are meant to be in the subscript)
So, if I found that ß1 was equal to -0.8, this would mean that for an increase in current prices of 1 %, ticket demand in the same period would decrease by 0.8 %. But what if I used detrended data for the price instead of the original ones. Would the interpretation of ß1 then stay the same or would it be somehow different?
The same question arises if I need to take the first difference (or higher differences) of data to make them stationary. How does that change the interpretation of the resulting betas?
Many thanks in advance!