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This might seem very elementary or even silly, but all comments are much appreciated. As science major I do not have deep technical knowledge in statistics, so any guidance is much appreciated.

Say we have this hypothetical problem:

Say I would like to come up with a model to predict returns of some financial instrument $I$ for a next day. I have the return values $R_n$ of the $I$ for the past $n$ days.

Additionally for each day $d$ I have some independent data $P_d$ (say $m$ numbers) that could be used to predict return value $R_d$ of today, but I have no idea what this data means and where it came from.

Are there any standard ways of finding how data $P_d$ relates to $R_d$, for example some kind of software package that loops through many possible models and check how well they fit?

Or what would be a way to tackle this type of problems, because it seems to me there could be infinite number of ways to use $P_d$ to predict $R_d$?

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Actually, I was thinking of posting a similar question, though coming from a different angle.

Firstly, your data $R_d$ and $P_d$ form a time series with potential interactions and you might end up using a vector autoregreesion methon (as in https://www.otexts.org/fpp/9/2)

In that case, you have to analyse all the auto-correlations and so on. Additionally, with a high dimensional $P_d$ you will get time series in a very high dimensional space.

So far I have no experience in the time-series regime, but this seems not very feasible.

Hence, one could also use a regression task that is fed with your data. You still might so enrich you data $P_d$ with additional features.

An advantage might be to use a nonlinear model, since they might find some structure in the data you don't see directly.

For example a neural network can be used as is pointed out in here or in here

You can also use a random forest as is pointed out here Note that here an optimization is performed to obtain the best parameters for moving averages that contain the data from previous events/time-steps

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