Difference variable question

[maavtc]

Hi,

I have what may be a really basic econometric question, but I would really appreciate anybody input.

Let's say I have a dependant variable that is stationnary (Y) and one independant variable that is not (economic activity measure, like gdp). I think the growth rate of X might have an impact on the level of Y and I want to measure it. Now the simplest model would be to using the differece of log X. I don't get a particularly good fit in that case because my data is montly and the monthly grow rate is too noisy.

What would be the options in those cases. Would it be acceptable to use the year over year growth rate for instance, or adding coefficients with more lags (t-1 minus t-2,t-2 minus t-3..etc).

I don't need a detailed answer, but would really appreciate if someone could point me in the right direction.

Thank you,