Prediction in Practice

English

Supervisor:

Introduction: For many recurring phenomena we suspect a kind of periodicity, but – strictly speaking – they are not periodic. For example, heart rate is not periodic, because each pulse lasts a bit differently. Course of daily temperature exhibits a kind of regularity, after lunch is warm and cold at night, but every day is different. And so on. The processing of such phenomena until recently resisted precise mathematical description. One interesting method for their description invented Huang some 15 years. This is referred to as EMD = Empiric Mode Decomposition or also Hilbert-Huang transform. Not much complex and has quite promising results. During EMD data are decomposed into a number (typically 15–20) of simple curves and each is treated separately. But at the beginning and end of the interval, EMD suffers from a big error. That's pretty annoying because what we need is an exact prediction of future course. The whole approach is relatively new, and is still under investigation. Therefore, I suppose that any positive results will be publishable in scientific journals.

The idea : It would be very interesting and necessary to make on-line web application (like in PHP or JAVA). The user will upload a file with the time course of a phenomenon; application performs EMD and displays the result. The user will be able to select various operating modes. Because it is an application designed for experimentation, it must be possible to change the options, the resulting graphs compare, change scale etc.. For inspiration, as the result could look like, are (for something else) see different stock charts. To those operating modes:

  1. EMD is done using spline interpolation. It is possible to select 3 options.
  2. by purpose:
  1. graph can constantly plot points as they come, and intercut between them curve
  2. graph may take some points, space them curve and extrapolate it to the chosen number of points in the future
  3. ditto, but will render extrapolation error
  1. renders the 3D graph of the instantaneous frequency (explain).

Students’ tasks: This topic is supposed spread into more works. The specific text of each task you will specify.