# Differencing in a simple OLS regression

I am attempting to do a simple OLS regression on time series data from 1990 to 2019, and there a trends in my variables GDP capita (dependent variable), oil prices etc which I am able to difference. I am not able to difference variables such as inflation as they are already stationary at level as demonstrated on Eviews. Is this acceptable in a model to have differenced variables and variables stationary and why? To offer context I am using the log of gdp per capita as my dependent variables with oil price as my main independent along with others such as net exports and inflation to calculate the impact of oil price on a net exporting country. I am not able to a VAR analysis as I have not been taught this as of this time. Any further help would be help that you assume would be helpful would be gratefully appreciated.

• You can't trust automated tests of stationarity, i.e. eViews. This is because the test is calculated on the univariate time series when in fact there are cross correlations that are not controlled for. Even if a time-series is not stationary, differencing won't necessarily remove the autoregressive effect. GDP should be inflation adjusted because that is the standard analysis of this kind of output. Variograms of residuals from OLS models should be compared to determine AR-1 autocorrelation, and fits for lagged effects of exposures should be considered. Feb 25 '21 at 21:42

(hi, im noob but

"Is this acceptable in a model to have differenced variables and variables stationary and why"

(for me, yes, because :

• ols requires stationarity, just because of mathematics inside of it
• like "constant mean"
• if inflation is stationary its ok
• if another vector (oil) is not stationary, you use diff and when its stationary its ok

as school task, i think you simple can answer ... ols requires all data (vectors) to be stationary

for example data 1 2 3 4 5 have trend and nonconstant mean ...so ols calculate this vector very bad ... but when we diff at lag 1, .. intercept is 1 and ar(1)=0 and model fit data like 100%