Parameter estimation for models of chaotic time series
We illustrate the inadequacy for chaotic time series data of widely-used dynamical parameter-estimation procedures based on whole-trajectory comparisons (“observation-error fitting”), using as case studies the record of measles outbreaks in New York City and simulated data generated by the logistic equation. We explore and reject alternative estimation methods based on matching emergent features of strange attractors; specifically, the Lyapunov exponents and the Hausdorff dimension. We show that partial-trajectory comparison methods (“process-error fitting”) work well when the system state is completely known through the course of the experiment.