Four different models were fit to the same time series. The first 100 time periods were used for the training period and the last 12 periods were treated as a validation period. Assume that the models make sense practically and fit the data reasonably well. Below are the RMSE values for each of the models:

Model A, Training Period RMSE = 543

Model A, Validation Period RMSE = 690

Model B, Training Period RMSE = 669

Model B, Validation Period RMSE = 675

Model C, Training Period RMSE = 670

Model C, Validation Period RMSE = 650

Model D, Training Period RMSE = 437

Model D, Validation Period RMSE = 375

1. Which model appears more useful for retrospectively describing the different components of this time series?

Model A

Model B

Model C

Model D

2.

1. Four different models were fit to the same time series. The first 100 time periods were used for the training period and the last 12 periods were treated as a validation period. Assume that the models make sense practically and fit the data reasonably well. Below are the RMSE values for each of the models:

   Model A, Training Period RMSE = 543

   Model A, Validation Period RMSE = 372

   Model B, Training Period RMSE = 754

   Model B, Validation Period RMSE = 640

   Model C, Training Period RMSE = 375

   Model C, Validation Period RMSE = 401

   Model D, Training Period RMSE = 437

   Model D, Validation Period RMSE = 420

   2. Which model appears to be more useful for forecasting purposes?

   Model A

   Model B

   Model C

   Model D