In my research, I focus on price differences between two regional markets. The price of market 1 is determined by a fundamental model while the price of market 2 is exogenous to this model. I consider different variants of the fundamental model and want to tell which model variant fits the data best. Now, I wonder whether I should compare the modeled price differences between the markets to historical price differences, or the modeled prices in market 1 to historical prices.
I used a linear regression (time series from different model setups regressed on historical data) in order to test which model fits the data best. If I use the price differences, I find that only the coefficient for one specific model variant is significant. However, if I use absolute price levels in market 1 for the comparison, I find significance for all modeled prices due to the common trend induced by the exogenous price in market 2. However, the level of significance between the model variants is different, i.e. the setup with significane for the price differences has also the highest significance when using price levels. Now, I am unsure whether I am really able to infer if one of the model variants describes the data best.