How to test difference among several time series using R

Question

i have many time series, each one representing a plant species. I think there is a pattern dependent on the woody density. High woody density species just flower between rain periods. Low woody density species flower in any periods.

With many species time series and measures of woody density, how do I model this with R to demonstrate this pattern?

Here is an example of what the data looks like:

#Woody Density
set.seed(69)
wden<-round(c(rnorm(5,mean=50),rnorm(5,mean=90)))
names(wden)<-c(paste("sp",1:10,sep=""))
wden

#Chuva
rain<-c(150,100,50,40,20,20,30,50,70,100,150,200,150,100,50,30,20,20,40,50,70,100,150,200)


#Flowering measures
ydet<-c(10,10,10,10,20,40,50,40,20,10,10,10)

#2 years for 5 low woody density and 5 high density species
flowering<-matrix(NA,nrow=24, ncol=10,dimnames=list(paste("month",1:24,sep=""),paste("sp",1:10,sep="")))
for (i in 1:5) {
               flowering[,i]<-round(c(ydet+rnorm(12,mean=5,sd=5),ydet+rnorm(12,mean=5,sd=5)),digits=2)
               }
for (i in 6:10) {
               flowering[,i]<-round(c(rnorm(12,mean=30,sd=5),rnorm(12,mean=30,sd=5)),digits=2)
               }
#Changing objects to Time series
flowering<-ts(flowering)
#Plot series
plot(flowering)

#Making colors for wood density
cores<-heat.colors(10,alpha=1)
matplot(c(1:24),flowering,type="l",lwd=2,lty=1,xlab="Time",ylab="Flowering",col=cores[order(wden)])

#Plotting Rain Together with time series
bargraph<-barplot(rain/max(rain)*100,xlab="Time",ylab="Rain")
matlines(bargraph,flowering,type="l",lwd=2,lty=1,xlab="Time",ylab="Flowering",col=cores[order(wden)])
axis(1,at=bargraph,labels=1:24)
axis(4,at=seq(0,100,by=10))

Ben Bolker · Accepted Answer

I might actually suggest you try this on http://stats.stackexchange.com, or on the r-sig-ecology@r-project.org mailing list. It's a little bit of a can of worms. The fundamental problem is that it's hard to prove that the association of two time series is causal, since (especially when both fluctuate regularly over time) it's easy for them to simply be fluctuating at about the same period and hence to appear to line up (the classic examples of this are the sunspot cycle and various totally unrelated time series like the New York stock exchange).

The classical approach to this would be to "whiten" each of the time series (you could fit a periodic spline or a sinusoidal model or just take differences of the pattern from the seasonal average) independently until each one is indistinguishable from white noise, then examine the cross-correlations among the time series (at lag zero, i.e. regular correlations, or at other lags to represent a leading/following pattern). In your case you would then presumably want to see how the cross-correlations varied in turn with wood density.

Alternatively, you could just lump the data into "rainy season" and "dry season" and do a more standard analysis (you get rid of most of the correlation by lumping), but (1) it would be nice to have an a priori division of seasons rather than doing it by looking at the data; (2) you might lose some power and/or interesting fine-scale patterns this way; (3) some of the basic inferential problems are still there -- is flowering associated with rain, or just with the rainy season?

Nice example, though.

How to test difference among several time series using R

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