Modelling Chaotic Data

TL;DR

This paper explores various methods for modeling chaotic data, focusing on their applicability, computational complexity, and accuracy, with detailed investigation into Measure-based Reconstruction and comparison of different models.

Contribution

It provides a comparative analysis of modeling techniques for chaotic time series, including an in-depth evaluation of Measure-based Reconstruction.

Findings

Measure-based Reconstruction shows promising accuracy for chaotic data

Different modeling methods vary in computational cost and suitability

Model testing and comparison are crucial for selecting appropriate techniques

Abstract

This paper extends the subjects dicussed in the Data Analysis and Dynamical Systems courses by looking at the subject of modelling data. This task is nontrivial as the underlying process could be non-linear. In the paper some common methods, including global and local polynomial fitting, are discussed in terms of their applicability, level of computation and accuracy. One example method, Measure based Reconstruction, has been investigated in greater detail and experimentation is carried out to evaluate the method. In this project we shall be looking at the different ways one can model chaotic time series. The reason we are going to look at a range of methods is that different methods are "good" for different applications. As the "goodness" of a model is subjective to the task one wishes to do, we will investigate a selected models and compare the prediction to see how one goes about testing a model.