Time series approximation with multiple dynamical system's trajectories. Forecast and control of the Internet traffic
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Utilization of multiple trajectories of a dynamical system model provides us with several benefits in approximation of time series. This method can employ equations of relatively low complexity and produce a better precision than the traditional models (ARIMA, VAR, Holt-Winters). The dynamical system's phase portrait analysis helps to see if the equations properly describe the reality. Different limit points of the phase portrait characterize various scenarios of the process' realization and switches of the behavioral patterns (influenced by externalities). We extend the dynamical systems approach (discussed in <cit.>) to the dynamical systems with 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.
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