Linear and nonlinear dynamic systems in financial time series prediction

Nonlinear Time Series in Financial Forecasting

Modelling and Prediction of Financial Time Series

We consider statistical aspects of the modelling and prediction theory of time series in one and many dimensions. We discuss Lévy-based and general models, and the stationary and non-stationary cases. Our starting point is the recent pair of surveys, Szegö’s theorem and its probabilistic descendants and Multivariate prediction and matrix Szegö theory, by this author.

Nonlinear Dynamic Boltzmann Machines for Time-Series Prediction

The dynamic Boltzmann machine (DyBM) has been proposed as a stochastic generative model of multi-dimensional time series, with an exact, learning rule that maximizes the log-likelihood of a given time series. The DyBM, however, is defined only for binary valued data, without any nonlinear hidden units. Here, in our first contribution, we extend the DyBM to deal with real valued data. We present...

Genetic Programming for Financial Time Series Prediction

This paper describes an application of genetic programming to forecasting financial markets that allowed the authors to rank first in a competition organized within the CEC2000 on “Dow Jones Prediction”. The approach is substantially driven by the rules of that competition, and is characterized by individuals being made up of multiple GP expressions and specific genetic operators.

Which Methodology is Better for Combining Linear and Nonlinear Models for Time Series Forecasting?

Both theoretical and empirical findings have suggested that combining different models can be an effective way to improve the predictive performance of each individual model. It is especially occurred when the models in the ensemble are quite different. Hybrid techniques that decompose a time series into its linear and nonlinear components are one of the most important kinds of the hybrid model...