Time-Delayed Embedding project

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CSSS 2006 Santa Fe

We propose to engage in a study of time series prediction of complex systems. Inspired by the talk of Liz Bradley, we would like to learn the technique of Time-Delay Embedding. The goal of the proposed project is to implement the time-series prediction technique used by Sauer in the Santa Fe Competition (Weigend & Gershenfeld, 1992), which featured the Time-Delayed Embedding.

The project will have two main parts, one that will focus on a study of a simple system (where we could learn the technique) and second that would be a study of more complex data set. A brief description of the two parts follows.

1. We propose to use a double-pendulum as a system that can be simulated using a simple model, and yet has interesting enough dynamics. This part will include these steps:

  • Creating the model of the double-pendulum (which has four dimensional state space)
  • Use the model to generate a time series of a pendulum simulation
  • Use the technique of time-delayed embedding of one of the state space variables from part of the time series data
  • Predict the system behavior into the future and compare it with the actual simulation (the second part of the time series)

2. Once we understand how the technique works on the simple model, we propose to use it to analyze data coming from real-world processes. The specific source of the data will be identified later, but possible suggestions include packet-level data from TCP network transmissions, or air-flow vortex formations around airplanes, both of which have been shown to have a very complicated dynamics.

David Rojas, Marko Thaler, Lukas Kroc