  The models VAR, ARIMA, Holt-Winters, are frequently used for short-term
forecasts of multivariate time series. In this paper we consider models
constructed with the help of dynamical systems that have relatively simple
limiting behavior. Switching between different trajectories of the phase
portrait, we obtain a high precision prediction. Moreover, the dynamical system
approach provides the global qualitative picture of the model's phase portrait,
and allows us to discuss multidimensional patterns and long-term properties of
the process. The simple limiting behavior allows us to associate different
trends with different process's realization scenarios that can be influenced by
externalities.
  We demonstrate these ideas using the examples of the Wikipedia's traffic of
Readers, Contributors and Edits. First, we consider the two-dimensional model,
predicting the traffic of Readers and Edits. The prediction precision is higher
than the two-dimensional VAR prediction. Different trends (corresponding to
different 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 accurate
short-term prediction of Edits than the two-dimensional dynamic model. The
global picture shows that the number of new Edits tends to decline in the
future, while the number of new Contributors and Readers will grow in the long
run.
