Suppose you perform a forecasting procedure on a time series, where the units of the time series values are dollars. You get the usual three measures of the forecast errors: MAE, RMSE, and MAPE. Now suppose you scale the time series to be in thousands of dollars and then run the same forecasting procedure on the scaled series. Which of the following is true?

a. The RMSE for the scaled series is the original RMSE divided by 1,0002.

b. The MAE for the scaled series is the original MAE divided by 1,000.

c. The MAPE for the scaled series is the original MAPE divided by 1,000.

d. All of these choices are true.