Best common metric for comparing classic time series forecasting methods (ARIMA/Prophet) with ML approach? I am new to time series forecasting and looking to compare the performance of ARIMA/Prophet with an XGBoost model in predicting future stock market values based on historical stock market data and social media sentiment scores.
I am more familiar with ML, so would usually use an evaluation metric like R^2 to assess model performance for this sort of problem.
Are there any common evaluation metrics which forecasting methods like ARIMA/Prophet use to assess their accuracy, so I can do a like-for-like comparison with the XGBoost's prediction accuracy?
In general the most common metrics mentioned in several articles (e.g. like this one) are the same we also commonly use for non-time series prediction:

MAE Mean absolute error
MSE Mean squared error
RMSE Root mean squared error

Outside of linear regressions I have not seen R² used that often to validate prediction models. In fact it isn't even one of the out-of-the-box metrics of xgboost for interval scale prediction tasks. So you should be fine using RMSE for everything.
Edit:
Prophet at least in the R package covers RMSE, MAE and MAPE so you should be fine.