Multivariate time series approximation by multiple trajectories of a dynamical system. Applications to Internet traffic and COVID-19 data

Utilization of multiple trajectories of a dynamical system model provides us with several benefits in approximation of time series. For short term predictions a high accuracy can be achieved via switches to new trajectory at any time. Different long term trends (tendency to different stationary points) of the phase portrait characterize various scenarios of the process realization influenced by externalities. The dynamical system's phase portrait analysis helps to see if the equations properly describe the reality. We also extend the dynamical systems approach (discussed in \cite{R5}) to the dynamical systems with external control. We illustrate these ideas with the help of new examples of the rental properties HOMES.mil platform data. We also compare the qualitative properties of HOMES.mil and Wikipedia.org platforms' phase portraits and the corresponding differences of the two platforms' users. In our last example with COVID-19 data we discuss the high accuracy of the short term prediction of confirmed infection cases, recovery cases and death cases in various countries.