Equilibrium properties of chaos Dr Rodney Wolff Chaotic processes, whilst completely deterministic, can appear to be very erratic or random. A completely non-parametric method is being developed to estimate such distributions. The method will be applied to small sections of exchange rate time series to measure the extent of stationarity and determinism in such data. The effect of violations of these conditions on chaotic dynamics, for example, by using a median filter, are being studied. The aim is to establish to what extent the dynamics of a chaotic time series are changed by non-linear filtering, and if they can be recovered.
Applications are in engineering, where median filtering is applied to various kinds of signals.
The relationship with stochastic volatility is explored. Many real physical systems, such as environmental, engineering and financial, can be described in terms of partial differential equations. This project incorporates non-parametric statistical methods with grid methods for solving PDEs, using recursion based on the deterministic dynamics, in order to avoid expensive computation yet to achieve solutions that are accurate and simultaneously sympathetic to the theoretical dynamics of the data. R.C. Local linear kernel estimation for discontinuous nonparametric regression functions . Communications in Statistics-Theory and Methods .