How to compare AR and ARIMA models?

Question

Relatively new to stats. I use linear regression and get R^2, which is quite low.

MODEL 1

    lmoutar=lm(formula = ts_y ~ ts_y_lag + ts_x)

So switched to arima with external regressor. Using "auto.arima", I formulate arimax model

MODEL 2

    fitarima <- auto.arima(ts_y, xreg=ts_x)
    arimaout<-arima(ts_y,order=c(2,0,5),xreg=ts_x)

How can I compare the explanability of AR model with arima model. From the thread How can I calculate the R-squared of a regression with arima errors using R?, I understand R^2 is not an option for ARIMA.

From the thread Model comparison between an ARIMA model and a regression model, AIC/BIC is not the right criteria and MSE from forcast/predict can be possible criteria for comparison across AR and ARIMA model. Is MSE the best option for model comparison, if so how would I generate MSE for AR and ARIMA?

I tried to compare the above ar and arima model using anova, but I get following error message

anova.lm(lmoutar,arimaout)
   Warning message:
    In anova.lmlist(object, ...) :
            models with response ‘"NULL"’ removed because response differs from model 1

What does this error message mean?

EDIT

Thanks for the response so far and insight that AR is nested within ARIMA. How would one answer this question, if I rephrase as "How to compare AR, ARIMA and General Linear Models?". The first model I listed has AR(1) and independent variable; it is a general linear model. So how would I compare a GLM versus ARIMAX model? Any thing else besides MSE that I could use to judge between GLM and ARIMAX

Answer 1

I believe you can use some information criterion since ARIMAX nests AR. Regression is a different beast, hence the objection in the other post. The procedure that auto.arima uses to pick p and q is described here. It used AICc to pick the model.

Answer 2

Since the two models are nested. The AR model is just an ARIMA model with all the moving average coefficient restricted to 0. You could use a likelihood ratio test (But really any test in the same vein will do)