Ongoing and Future Work

After having gained experience in linear time series methods such as Vector Autoregressive modelling, I decided to learn about nonlinear methods, with the ultimate goal of nonlinear prediction and estimating extreme value statistics.

This has required groundwork in developing understanding of nonlinear dynamic behaviour and phase space reconstruction, involving embedding procedures, and where the time evolution of a dynamical system can be represented in geometric form. There are several measures of the fractal dimension or "strangeness" of these attractors.

The concept of "recurrence" allows one to study how systems, under certain conditions and after a sufficiently long time, return to a state "close" to the initial state. A graphical analysis through recurrence plots (RPs) of the m-dimensional phase space can be made in a 2D representation.

The method of surrogate data tests can be employed to distinguish between noisy linear stochastic dynamics as a likely driver or whether deterministic nonlinear structure is present. Noise obscures detection of systematic dynamic structure in data by decreasing the resolution of reconstructed attractors and increasing the embedding dimension required to capture underlying phase space dynamics.

Another factor to consider is the presence of slow moving trends so the data must be long enough to capture them. NLTS methods search for system dynamics likely to have generated observed irregularity in data. One signal processing technique that can be used to separate unstructured variation (noise) from structured variation (signal) is "singular spectrum analysis (SSA)". This may also eliminate detected nonstationarity by purging the signal of slow-moving trend components.

In future I hope to see how nonlinear prediction can be facilitated by reconstructing phase space using a method called time-delay embedding. It is hoped to be able to test such an approach in the field of windspeed prediction.