# How to compare ARIMA models with regressors?

How can i compare ARIMA models that use the same forecast variable, but different regressors? I am trying to find the best regressor for the Bitcoin price. For this i have collected several time-series.

On which value should i focus? AIC, AICc and BIC or the errors ME, RMSE, MAE, ...

For example

> fit.btcPrice <- auto.arima(xts_BtcPrice[2:133], xreg=regressors[2:133,2:2])
> summary(fit.btcPrice)
Series: xts_BtcPrice[2:133]
Regression with ARIMA(0,1,0) errors

Coefficients:
xreg
0.5437
s.e.  0.1358

sigma^2 estimated as 166344:  log likelihood=-972.81
AIC=1949.61   AICc=1949.71   BIC=1955.37

Training set error measures:
ME     RMSE      MAE        MPE     MAPE     MASE       ACF1
Training set -25.51915 404.7512 316.8867 -0.3933149 3.646035 0.976136 -0.0592231


VS.

> fit.btcPrice <- auto.arima(xts_BtcPrice[2:133], xreg=regressors[2:133,3:4])
> summary(fit.btcPrice)
Series: xts_BtcPrice[2:133]
Regression with ARIMA(1,0,2) errors

Coefficients:
ar1      ma1     ma2  intercept  twtcntLag1  sum_pos_neg
0.9198  -0.0537  0.2823  7968.0855      0.0058       0.4679
s.e.  0.0401   0.0881  0.1082   593.5162      0.0104       0.1106

sigma^2 estimated as 162654:  log likelihood=-977.38
AIC=1968.76   AICc=1969.67   BIC=1988.94

Training set error measures:
ME     RMSE      MAE        MPE     MAPE      MASE        ACF1
Training set -23.7281 394.0317 308.5825 -0.4697202 3.555831 0.9505559 -0.01568309<