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I have time series of several variables. Just in one specific case one variable is linear combination of the rest.

I want to predict probability distribution (that is not only best estimate but estimates with probability of that happening) of future value of variables. I want to see when probability of small interval of possible outcome is high.

A priory I don't know rules of the game how variables evolve and inter-depend.

What is the tool to best do such prediction and how easy is it? Will scikit-learn do? Maybe neural networks?

ADDED based on answer:

As I've understood, time series theory data science assumes random walk, however I assume variables are at least partly moved by free will of players of the game under some a priory unknown to me constraints and goals.

Should statistical solution advised work in such case? Can data predict reversal of possible current trend?

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    $\begingroup$ Welcome to DataScience.SE! Look into Gaussian process regression and Bayesian time series forecasting. $\endgroup$ – Emre Jul 14 '16 at 0:37
  • $\begingroup$ @Alexei Pls explain what you mean by "small interval of possible outcome". This question way too broad. You need to provide more description of the process from which you collected this data. $\endgroup$ – horaceT Jan 8 '17 at 4:16
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Yes, you can use scikit-learn for this use case. You may find this tutorial useful.

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  • $\begingroup$ Shagun, thank you. However, first, I could not find how to get probabilities of estimations, second, looks to me all time series theory assumes random walk, however I want to check hypothesis if variables are at least partly moved by free will of players of the game under some unknown to me constraints and goals, third, IMHO as I do not assume randomness, I cannot detrend etc. I will edit my question. $\endgroup$ – Alexei Martianov Jun 11 '16 at 15:28
  • $\begingroup$ I would say you try with different models like linear regression and see which one works for you. Your problem is more concerned with finding the correct model and not the correct tool to implement it. So basically you start with some estimations and see if the estimations and assumptions hold and then you refine. $\endgroup$ – Shagun Sodhani Jun 11 '16 at 16:27
  • $\begingroup$ @ShagunSodhani This is not an answer to OP question. It's like saying please read a book on time series. $\endgroup$ – horaceT Jan 8 '17 at 4:17
  • $\begingroup$ @horaceT the original question was: What is the tool to best do such prediction and how easy is it? Will scikit-learn do? Maybe neural networks? I replied by saying Yes, you can use scikit-learn for this use case.. I further added a link to a tutorial which shows how probability distribution for a time series may be predicted. I do not see how this is not an answer. I am not being rude, just trying to see how I may improve :) $\endgroup$ – Shagun Sodhani Jan 8 '17 at 6:02

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