Towards a framework for combining stochastic and deterministic descriptions of nonstationary financial time series

Abstract

We present in this paper ideas to tackle the problem of analysing and forecasting nonstationary time series within the financial domain. Accepting the stochastic nature of the underlying data generator we assume that the evolution of the generator's parameters is restricted on a deterministic manifold. Therefore we propose methods for determining the characteristics of the time-localised distribution. Starting with the assumption of a static normal distribution we refine this according to the empirical results obtained with the methods and conclude with the indication of a dynamic non-Gaussian behaviour with varying dependency for the time series under consideration.