Trend estimation in vector time series with long-range dependence

We present a method for efficient estimation of trend coefficients in a multivariate regression with cross-correlated long-range dependent errors. The method is semi-parametric in that the exact correlation structure of the errors need not be specified, only the low-frequency behavior. The trend coefficients and long-range dependent parameters are estimated simultaneously. The method is used to detect anthropogenic trends in mean temperatures for the Northern and Southern Hemispheres, allowing for persistence and cross-correlation in the random error components.