Nonchaotic Models and Predictability of the Users' Volume Dynamics on Internet Platforms

TL;DR

This paper introduces a nonchaotic dynamical system approach to model and predict long-term user volume dynamics on internet platforms, offering more reliable insights than traditional short-term time series models.

Contribution

It proposes a novel nonchaotic dynamical system framework for modeling platform traffic, enabling qualitative analysis and long-term prediction of user behavior.

Findings

Models are nonchaotic with reliable long-term predictions.

Applicable to various platforms like Amazon, Wikipedia, and military sites.

Reconstruction of differential equations from data is demonstrated.

Abstract

Internet platforms' traffic defines important characteristics of platforms, such as price of services, advertisements, speed of operations. The traffic is usually estimated with the help of the traditional time series models (ARIMA, Holt-Winters, etc.), which are successful in short term extrapolations of sufficiently denoised signals. We propose a dynamical system approach for the modeling of the underlying process. The method allows to discuss the global qualitative properties of the dynamics' phase portrait and long term tendencies. The proposed models are nonchaotic, the long term prediction is reliable, and it explains the fundamental properties and trend of various types of digital platforms. Because of these properties, we call the flow of these models the {\it trending flow}. Utilizing the new approach, we construct the two-sided platform models for the volume of users, that can be applied to Amazon.com, Homes.mil or Wikipedia.org. We consider a generalization of the two-sided platforms' models to multi-sided platforms. If the equations' are cooperative, the flow is trending, and it helps to understand the properties of the platforms and reliably predicts the long term behavior. We show how to reconstruct the governing differential equations from time series data. The external effects are modeled as system's parameters (initial conditions).