[R] correlation coefficient of ARIMA() or GLS() ?

[Jan Verbesselt]

Hi R-helpers,

I fitted the following ARIMA model onto de-seasonlised time series 1 and
2, which were strongly seasonal. How can the R² or the coefficient of
determination for the structural term be calculated between these two
fitted time series? 

Is an GLS() the solution (difference between ARIMA and GLS) ? Is it
possible to calculated an R² from a GLS() model ? # nlme and MASS
package


***************************
reg.model <- arima(serie2.dd, order=c(6,0,0), xreg = serie1.dd, method =
"ML") 
tsdiag(reg.model)  #  =>looks OK. residuals are not autocorrelated
(ljung-box statistic)  but not normally distributed.Problem?

> reg.model
Call:
arima(x = serie2.dd, order = c(6, 0, 0), xreg = serie1.dd, method =
"ML")
Coefficients:
         ar1     ar2     ar3     ar4     ar5     ar6 intercept serie1.dd

     -0.1033 -0.3957 -0.0423 -0.2719 -0.2969 -0.1401   -2.3535  585.9007
s.e.  0.0843  0.0823  0.0831  0.0857  0.0795  0.0829    3.1520  118.1323

sigma^2 estimated as 6932:  log likelihood = -829.9,  aic = 1677.79
>

gls.ddm2 <- gls(serie2.ddm ~ serie1.ddm -1, correlation=corARMA(p=6),
method="ML") # fit of a gls without intercept because the intercept was
not significant but residuals are still auto correlated...?!
****************************************************

Tips, advice or examples are mostly welcome.
Many thanks in advance,
Regards,
Jan

_____________________________________________________________________
Jan Verbesselt 
Research Associate 
Lab of Geomatics and Forest Engineering K.U. Leuven
Vital Decosterstraat 102. B-3000 Leuven Belgium 
Tel:+32-16-329750   Fax: +32-16-329760
http://gloveg.kuleuven.ac.be/