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

Abstract

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.