Let's say you have a dependent variable and many independent variables. What are the preferred metrics for sorting and selecting variables based on explanatory power? Let's say you are not concerned with correlation among your inputs.
My thoughts are below. Let me know if I'm missing anything obvious, or if there is a metric that you feel dominates the others.
- Spearman correlation controlling for sector
- Granger causality
- Johansen test for cointegration
- Grinold's Information Ratio
- Economic performance of the factor during a factor backtest (i.e. drawdown, sharpe, etc.)
- Volatility of the factor premium
- Persistency of the factor premium
- Monotonic relation test
- Significance test on spread return (Q5-Q1) vs. Mean Return
- R^2 of factor after building some kind of model
My preference would be correlation coefficient.