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Quartz | Level 8
Dear Time Series/Regression Experts:

Is it econometrically sound/okay to use non-stationary independent variables in a time-series (ols) regression? Here's the following delimma/options using the same starting raw/untransformed original data series:

1. I have a regression whereby the dependent variable and independent variables are all stationary (let's say using log difference transformation for all dependent and independent variables). However, then the R squared value from the regression is very low (below 0.20). Coefficients of all variables are statistically significant and regression residuals are stationary and normally distributed.

2. I can run a regression whereby the dependent variable "is" stationary but independent variables are not stationary. However, the R Squared value is much better (>0.40). Coefficients of all variables are statistically significant and regression residuals are still stationary and normally distributed.

3. I compare the final forecasts of the raw/untransformed data resulting form 1 and 2 and and they are very similar.

Below are my questions:

Is the 2nd model econometrically sound? Are there any published papers to support this? I found an interesting article about "ovedifferencing" by Professor Cochrane which argues that when we overdifference, much of the variation in the data can be thrown out. ... encing.pdf

Any latest research suggests option 2 is "okay"?




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