Testing for common deterministic trend slopes

We propose tests for hypotheses on the parameter for deterministic trends. The model framework assumes a multivarariat stucture for trend-stationary time series variables. We derive the asymptotic theory and provide some relevant critical values. Monte Carlo simulations suggest which tests are more useful in practice than others. We apply our tests to examine if monthly temperatures in the Netherlands, measured from 1706 onwards, have a trend and if these trends are the same across months. We find that the January and March temperatures have the same upward trend, that the September temperature has decreased and that the temperatures in the other months do not have a trend. Hence, only winters in the Netherlands seem to get warmer.