Stationary data first after the 2-order/3-order difference on LN(variable)


New Member
I want to make an Linear Regression.
Dependent variable: GDP
Independent variables: Net exports and Debt and some control variables
All variables are seasonal and calendar adjusted.

The aim it to see the effects of Next export and Debt on GDP for different european countries. I will make two regressions for each country, 1 regression with data from 2000-2007 and 1 regression from with data from 2008-2016 (using quarterly data).

I have transformed all variables into Natural logarithm differences, mainly for interpretation purposes but also to obtain stationary data. However, non of the variables are staionary neither in level or in natural log differences.

They first become stationary when I take the second-order or third-order difference of the natural logarithm (after the first difference in natural log, no trend can be found).

Q1) Can I use the variables in second-order/third-order differences of natural logarithm in a linear regression?
If yes, can I mix variables with second-order diff. with variables with third-order diff. in one model?
If yes, is the interpretation of these variables the same as in first order differenced of natural logarithm?

Many thanks in advance!