# Predicting time series based on another

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:

1. Split data into training/testing.

2. 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)

3. Compute pearson correlation across different lags of $$X$$, find the highest value.

4. Find out if you're over-fitting or not by testing that lag with the test dataset.

5. ???? How do i then use this information. Let's say pearson correlation is 0.45 with a p-value of 2e-9 on 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?

TL;DR -

• 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?