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
