What branch of data science to use for revealing preceding conditions of desired outcome

On financial data series, I would like to determine if some conditions precede a desired outcome.
For example, let’s take as an example the daily data of a stock. On some days, the stock experience big trends.
I would like to know if conditions on preceding days, such as volume, day ranges, price moving average… plus many others occur with any statistical significance to have a predictive value.

So I have an outcome (large trending days), a list of preceding conditions (can be a big list), and would like to know if some relation exists.
Ideally I want to specify as much preceding conditions as possible, and have the system discover statistically significant correlations with the occurence of the outcome.

What branch/sub-branch of data science should I explore? A branch of statistics? Supervised Machine Learning? Unsupervised?