[R] [OT] testing for synchronicity

[Andrew Robinson]

Greetings, friends in the R community,

this is an OT question about statistics. Given four time series of
events, what possibilities do I have to test for synchronicity?

e.g.

times <- data.frame(year=   c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10),
		    event.1=c(1, 0, 0, 1, 2, 4, 1, 0, 0, 0),
		    event.2=c(0, 0, 0, 1, 0, 2, 1, 0, 0, 0),
                    event.3=c(1, 0, 0, 0, 1, 2, 4, 1, 0, 0),
                    event.4=c(0, 1, 0, 1, 0, 0, 1, 1, 1, 0))

I have about 100 years of each, and my null hypothesis is that the
events are not synchronous. 

Right now my thinking is to focus on pairwise comparisons:

1) ignore the magnitude and convert the series to binary  
 
2) the sum of the product of the events of any two years is then the
   number of overlapping occurences.

3) I think that, in the absence of temporal autocorrelation, I could
   assume that this sum is hypergeometrically distributed.

4) I can test for statistical significance of this number by a moving
   blocks monte-carlo simulation.  I will do this by taking blocks of
   contiguous years with a random start and reordering them
   randomly.  This conditions on the number of event occurrences,
   which I would rather do than have it be random, and partially
   preserves the temporal autocorrelation.
   

If anyone has any thoughts, or pointers, they'd be very welcome.

Cheers

Andrew
-- 
Andrew Robinson  
Department of Mathematics and Statistics            Tel: +61-3-8344-9763
University of Melbourne, VIC 3010 Australia         Fax: +61-3-8344-4599
Email: a.robinson at ms.unimelb.edu.au         http://www.ms.unimelb.edu.au