Using exogenous variables in testing for monotonic trends in hydrologic time series

One approach that has been used in performing a nonparametric test for monotonic trend in a hydrologic time series consists of a two-stage analysis. First, a regression equation is estimated for the variable being tested as a function of an exogenous variable. A nonparametric trend test such as the Kendall test is then performed on the residuals from the equation. By analogy to stagewise regression and through Monte Carlo experiments, it is demonstrated that this approach will tend to underestimate the magnitude of the trend and to result in some loss in power as a result of ignoring the interaction between the exogenous variable and time. An alternative approach, referred to as the adjusted variable Kendall test, is demonstrated to generally have increased statistical power and to provide more reliable estimates of the trend slope. In addition, the utility of including an exogenous variable in a trend test is examined under selected conditions.