I have an econometric dataset, 50 observations of 350 variables. They include things like GDP, unemployment, interest rates and their transformation such as YoY change, log transform, first differences etc. I need to build an arimax model, and first I need to select variables.
350 univariate regressions against the response were run, and the 20 best predictor variables based on R-square were chosen.
My question is: is univariate regression a good way to screen predictor variables? I have read that variables perform differently in the when combined with others than alone. Is there anything I need to check about my data before pruning my set of predictor variables this way? ( My response variable is a log return (whose mean is close to zero), the transformed predictor variables vary in scale: some in log scale , others range in 100,000s. I expect most of the transformed ones to be stationary. )
Also, I tried running a Lasso selection in SAS with all the variables, and Lasso terminated in just 1 step selecting one variable only. There was a message whichi said that only 5 records out of the 50 observations were used by Lasso. Could this be due to missing values? My data doesn't have too many missings, so I was surprised. Maybe its because there are far many more predictors than observations (350 vs 50 ).
Thanks for any advice on how to proceed.