A prediction scheme for spatio-temporal time series is presented that is based on reconstructed local states. As a numerical example the ev olution of a Kuramoto-Siv ashinsky equation is forecasted using previously sampled data.

There has been growing interest in developing nonlinear dimensionality reduction algorithms for vision applications. Although progress has been made in recent years, conventional nonlinear dimensionality reduction algorithms have been designed to deal with stationary, or independent and identically distributed data. In this paper, we present a novel method that learns nonlinear mapping from tim...

Within the last years several methods for the analysis of nonlinear autoregressive time series have been proposed. As in linear autoregressive models main problems are model identification, estimation and prediction. A boosting method is proposed that performs model identification and estimation simultaneously within the framework of nonlinear autoregressive time series. The method allows to se...

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In this thesis a previously developed framework for modelling diversity of approximately periodic time series is considered. In this framework the diversity is modelled deterministically, exploiting the irregularity of chaos. This is an alternative to other well established frameworks which use probability distributions and other stochastic tools to describe diversity. The diversity which is to...

We introduce a nonparametric nonlinear time series model. The novel idea is to fit a model via penalization, where the penalty term is an unbiased estimator of the integrated Hessian of the underlying function. The underlying model assumption is very general: it has Hessian almost everywhere in its domain. Numerical experiments demonstrate that our model has better predictive power: if the unde...

Recent developments in nonlinear time series modelling are reviewed. Three main types of nonlinear model are discussed: Markov Switching, Threshold Autoregression and Smooth Transition Autoregression. Classical and Bayesian estimation techniques are described for each model. Parametric tests for nonlinearity are reviewed with examples from the three types of model. Finally forecasting and impul...

In this paper we provide conditions for nonlinear time series to be geometrically explosive with positive probability. The paper complements earlier work by the authors on geometrically ergodic nonlinear time series, showing that the conditions for examples in the earlier paper are sharp. We also study the transience of polynomial autoregression models.

Many dynamical phenomena in nature as well as in technological applications involve nonlinear behaviour as an essential ingredient. This fact is reflected by recent developments in time series analysis. Rather than attempting to give a comprehensive review in this limited space, I will report on one example of a novel method that can take nonlinearity into account without assuming determinism. ...

In this article, algorithms of non-linear filtering of Poisson time series are tested using statistical modelling. The objective is to find a representation of a time series as a wavelet series with a small number of non-linear coefficients, which allows distinguishing statistically significant details. There are well-known efficient algorithms of non-linear wavelet filtering for the case when ...