Modelling and forecasting the behavior of multi-fractal time series: Can we forecast the future?

  • Vladimir Kulish
  • Rushikesh Pawar


Time records of many processes can be viewed as fractal time series (e.g. pressure and temperature fluctuations, biological signals such as EEG, value fluctuations on the stock market, etc.). Understanding and forecasting the behaviour
of such time series is a very important but an extremely challenging task. A novel mathematical model, based on phase-lagging and fractional partial differential equations, can satisfactory describe major trends within multi-fractal time series. The
model allows one to obtain the Volterra-type integral equations that relate the evolution of the value (e.g. temperature, price) with the localised energy flux that causes this evolution. It seems also that the dynamic analysis of the fractal measures
of many time series can become a useful tool to forecast the behaviour of the latter.