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

TL;DR

This paper introduces dynamical systems-based models for multivariate time series prediction, demonstrating higher accuracy than traditional methods like VAR and ARIMA on Wikipedia traffic data, with insights into long-term patterns.

Contribution

It presents a novel dynamical systems approach for multivariate time series forecasting, capturing global qualitative behavior and long-term trends, outperforming standard statistical models.

Findings

Dynamical models outperform VAR in traffic prediction accuracy.

Different process scenarios relate to external influences and trends.

Long-term analysis shows declining Edits and increasing Readers and Contributors.

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.