We discuss how nonstationarity in observed time series data due to pronounced fluctuations of system parameters can be resolved by making use of embedding techniques for scalar data. If a D-dimensional deterministic system is driven by P slowly time dependent parameters, a (D+P)-dimensional manifold has to be reconstructed from the scalar time series, which is done by an m>2(D+P)-dimensional time delay embedding. We show that in this space essential aspects of determinism are restored. We demonstrate the validity of the idea heuristically, for numerical examples and for human speech data.

We propose a way to automatically detect the best neighborhood size for a local projective noise reduction filter, where a typical problem is the proper identification of the noise level. Here we make use of concepts from the recurrence quantification analysis in order to adaptively tune the filter along the incoming time series. We define an index, to be computed via recurrence plots, whose minimum gives a clear indication of the best size of the neighborhood in the embedding space. Comparison of the local projective noise reduction filter using this optimization scheme with the state of the art is also provided.

A local projective noise reduction scheme, originally developed for low-dimensional stationary deterministic chaotic signals, is successfully applied to human speech. This is possible by exploiting properties of the speech signal which resemble structure exhibited by deterministic dynamical systems. In high-dimensional embedding spaces, the strong inherent nonstationarity is resolved as a sequence of many different dynamical regimes of moderate complexity.

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Abstract.Starting from the observation of the real trading activity, we propose a model of a stockmarket simulating all the typical phases taking place in a stock exchange. We show that there is no need of several classes of agents once one has introduced realistic constraints in order to confine money, time, gain and loss within an appropriate range. The main ingredients are local and global coupling, randomness, Zipf distribution of resources and price formation when inserting an order. The simulation starts with the initial public offer and comprises the broadcasting of news/advertisements and the building of the book, where all the selling and buying orders are stored. The model is able to reproduce fat tails and clustered volatility, the two most significant characteristics of a real stockmarket, being driven by very intuitive parameters.