1
$\begingroup$

Say I have a numeric sequence A and a set of sequences B that vary with time.

I suspect that there is a relationship between one or more of the B sequences and sequence A, that changes in Bn are largely or wholly caused by changes in sequence A. However there is an unknown time delay between changes in A and their effect on each of the B sequences (they are each out of phase by varying amounts)

I am looking for a means of finding the most closely correlating B to A regardless of the time delay. What options are available to me?

** EDIT **

The crux of the problem here is that I have millions of B sequences to test, and there are approx 2 million data points within the lag window that I would like to test over. Working out a correllation for each B for each possible lag scenario is just going to be too computationally expensive (especially as in reality there will be a more dynamic relationship than just lag between A and B, so I will be looking to test variations of relationships as well).

So what I am looking for is a means of taking the lag out of calculation.

  • 1
    I think the [cross-correlation of signals](http://en.wikipedia.org/wiki/Cross-correlation) is a relevant concept here, even if it may not directly solve your problem.2010-12-01
  • 0
    Then, I think you should look for PCA or Principal Component Analysis or some variant of it. I suggest you ask on [CrossValidated](http://stats.stackexchange.com/). That's where the statistics experts are hanging out. They will know what the best options are. Besides, it seems to me you are not interested in the mathematical reasoning behind validity of the method, you just want a ready-made solution.2010-12-02
  • 0
    Hey no, sorry, I am grateful for your very detailed response, it is my fault for not being clear about the problem. The reasoning is v important to me though as for performance I may need to take shortcuts and I need to understand what consequences they may have. I will check out PCA.2010-12-02
  • 0
    Have you asked on [CrossValidated](http://stats.stackexchange.com/)?2011-01-01

3 Answers 3