Suppose I want to predict future changes in variable y (stock price over time). I notice that variable x1, inverted and delayed three months, tends to lead y. Which technique can I use to find other predictive relationships like this? Suppose I have variables x2 through x100 that I want to analyze to see if they also lead y in some way.
What are the non-machine learning (ie traditional statistical) options? Do the machine learning ones work better?
Context: want to predict future changes in S&P 500 price based on other assets like gold, oil, currencies, etc.