3
$\begingroup$

I have a large number (hundreds to thousands) of noisy time series that represent contemporaneous observations from different subjects.

I hypothesise that there exist lead-lag relationships between observations for different subjects (or groups of subjects.)

I would like to explore the potential use of such lead-lag relationships for the purposes of predicting the individual series.

What methods might I consider for this?

edit: To be clear, I am not looking at pairwise relationships. What I am looking for is a method that would look at the mountain of data at hand and attempt to discover (potentially non-linear) lead-lag relationships between arbitrary groups of series and the individual series to be predicted.

$\endgroup$
  • 1
    $\begingroup$ Read more about VAR models and Granger causality tests. They are used to estimate multivariate processes. $\endgroup$ – user158442 Apr 22 '17 at 23:58
8
$\begingroup$

You can choose from about 40 years of research and countless books, dissertations, monographs etc.

Given that your question is not all that focussed yet, maybe an introductory time-series book could help. In a nutshell, the autocorrelation function gives clues to lead/lag relationships that may be present in a single time-series, or between two series.

Rob has done a lot of research into sensibly automating the process of identifying how many / which leads/lags to use, so please look at his forecast package for R and other research.

| cite | improve this answer | |
$\endgroup$
0
$\begingroup$

http://en.wikipedia.org/wiki/Granger_causality

Barrett, Barnett & Seth have a paper which extends the idea of Granger causality to the multivariate case.

| cite | improve this answer | |
$\endgroup$
0
$\begingroup$

You should consider the Cross Correlation Function as that is meant to identify the lead/lag relationship. Dirk had mentioned the Autocorrelation Function, but that is meant for just one single time series and not for multivariate. You should consider looking at the Box-Jenkins textbook Chapter 10 where they introduce the steps do this.

You say your data is noisy, but if it has a pattern where the lead/lag response is strong then you will find significance.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.