[R] Different sings for correlations in OLS and TSA

[Michael Tiemann]

Dear list,

I am trying to re-analyse something. I do have two time series, one
of which (ts.mar) might help explaining the other (ts.anr). In the
original analysis, no-one seems to have cared about the data being 
time-series and they just did OLS. This yielded a strong positive
correlation.
I want to know if this correlation is still as strong when the 
autocorrelations are taken into account. There are autocorrelations, so
I model the data with arima() to get the parameters and fit it with
gls(). So far, the code seems to work fine, but what puzzles me is that 
I get different sings: the gls-fit yields a strong negative correlation.
This shouldn't be so, so I suspect I am doing something wrong.

Here is my code:

# this is my data
ts.mar<-ts(c(431.3,438,389.7,353.3,354.6,371.8,397.7,438.5,467.9,505.7,574.7,644.7,667.8,616.4,509.6,447,413.1,384.1),start=1980,freq=1)
ts.anr<-ts(c(104.1,102.4,97.9,96.2,95.1,95.1,97.9,101.6,105.9,111.1,117.9,121.3,121.8,114.2,107.6,105.1,101.9,98.6),start=1980,freq=1)
# to find autocorrelations via (p)acf's and mle I do:
fun.tsa.mle<-function(x){
par(mfrow=c(3,1))
acf(x)
pacf(x)
# AR model is estimated
m1<- ar.mle(x)
# An estimation of the unexplained portion of variance
m1.1<-m1$var.pred
# plot the function
plot(x)
# Give a printout
print(m1)
print("unexplained portion of variance:")
print(m1.1)
print("Mean:")
print(m1$x.mean)
par(mfrow=c(1,1))
}
#now, the autocorrelations should be consistent with following processes:
fun.tsa.mle(ts.mar)      #following DAAG a p=2 AR
fun.tsa.mle(ts.anr)      #following DAAG a p=2 AR
#I need to know, wether ts.anr can be explained with ts.mar, so
#according to ar.mle:
mod3<-arima(ts.anr,order=c(2,0,0),xreg=ts.mar,transform.pars=TRUE)
fit3 <- gls(ts.anr ~ ts.mar,correlation = 
corARMA(value=c(mod3$coef[1],mod3$coef[2]),p=2))
summary(fit3)
ts.plot(ts.anr,fit3$fitted,col=1:2)
#the puzzling bit is the negative correlation. It ought to be positive, 
I think.
#a simple OLS (this is what the people before me have done) yields
test3<-ols(ts.anr~ts.mar)
test3 #with a positive correlation. Why?


Where is the mistake? Up to now, I just thought time-series analyses 
would correct parameters and estimations, but simply changing signs?

Appreciating your help and suggestions,

Michael.