## 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.