This is more of a generic question, but I'm sure it has a best answer/methodology which is what I'm trying to reach. I'm trying to figure out a solid line of thought when looking at a time series X and seeing if it can predict some stock prices. I've gone through a few threads on this site.
The problem statement can be thought of as follows: given the daily closing prices of a stock, let's say AAPL, and an arbitrary predictor time series $X$ that is also given daily at close. Is $X$ a good predictor of AAPL's movement and how far in the future does it predict the price?
Here's what I've resolved to doing:
Split data into training/testing.
In order to make the time series stationary, you do first differencing on both time series. (i.e. compute the percent change for each period)
Compute pearson correlation across different lags of $X$, find the highest value.
Find out if you're over-fitting or not by testing that lag with the test dataset.
???? How do i then use this information. Let's say pearson correlation is
0.45with a p-value of
2e-9on the test dataset. Is this good? not good enough? How do I then trade on this information?
I've read online about the Granger-Causality test, which sounds like it could help here. But I'm also just not sure about a lot of the assumptions I'm making here. Is percent-change the way to do it? What are the cutoffs for good vs. bad correlations? Also, there are very little posts I could find online that go past this point. I'm not sure what the intuition is here. If they're correlated, and $X$ is found to have the highest lag around 3 days before. Then what do i do?
how do i best test causality/effectiveness of a given predictor series (transforming data+statistical tests)?
how do i find best lag for the test?
how do i then use this knowledge?