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The models VAR, ARIMA, Holt-Winters, are frequently used for short-termforecasts of multivariate time series. In this paper we consider modelsconstructed with the help of dynamical systems that have relatively simplelimiting behavior. Switching between different trajectories of the phaseportrait, we obtain a high precision prediction. Moreover, the dynamical systemapproach provides the global qualitative picture of the model's phase portrait,and allows us to discuss multidimensional patterns and long-term properties ofthe process. The simple limiting behavior allows us to associate differenttrends with different process's realization scenarios that can be influenced byexternalities.  We demonstrate these ideas using the examples of the Wikipedia's traffic ofReaders, Contributors and Edits. First, we consider the two-dimensional model,predicting the traffic of Readers and Edits. The prediction precision is higherthan the two-dimensional VAR prediction. Different trends (corresponding todifferent fixed points) can be associated with different platform's incentives.Then, adding the Contributors data, we discuss the three-dimensional model(more precise than the three-dimensional VAR). It provides a more accurateshort-term prediction of Edits than the two-dimensional dynamic model. Theglobal picture shows that the number of new Edits tends to decline in thefuture, while the number of new Contributors and Readers will grow in the longrun.

Dynamical systems' models for the prediction of multi-variable time series. Wikipedia's traffic example