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I want to perform an encompassing test in order to compare two simulation models, a Cournot model and a competitive model, in order to tell which model fits best to historical market data. The outputs of my model are prices as well as quantity decisions for two firms, i.e. three time series. I also have historical observations for all three time series. In applications of the encompassing test in the literature, I only found that one modelled time series was compared to a historical time series, e.g. modelled prices from two competing models to historical prices. Since I have three variables / time series, I wonder if I should apply three encompassing tests for each variable separately, or is there a way to compare modeled prices and quantities simultaneous to historical observations? I guess this would be something like a multi dimensional encompassing test.

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