Time series prediction by multivariate next neighbor methods with application to zooplankton forecasts

In the context of non-linear dynamics, next neighbor prediction methods have been successfully applied to univariate time series. We generalize these methods, in particular, center-of-mass-prediction (COM-prediction) and local linear prediction (LL-prediction), to multivariate time series. The use of multivariate prediction techniques is especially interesting when time series are short but several variables have been measured simultaneously. These additional variables can sometimes supply information to perform good predictions that otherwise could only be obtained from longer time series. In contrast to non-local prediction methods, next neighbor techniques are applicable to non-stationary time series. This is particularly valuable for time series obtained under non-laboratory conditions, as in environmental science, where boundary conditions are not controllable. The application of our methods to the prediction of zooplankton data, collected in the German North Sea close to Helgoland island, turns out to be promising.