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One major challenge in neuroscience is the identification of interrelations between signals reflecting neural activity. When applying multivariate time series analysis techniques to neural signals, detection of directed relationships, which can be described in terms of Granger-causality, is of particular interest. Partial directed coherence has been(More)
In this paper, we investigate the use of partial correlation analysis for the identification of functional neural connectivity from simultaneously recorded neural spike trains. Partial correlation analysis allows one to distinguish between direct and indirect connectivities by removing the portion of the relationship between two neural spike trains that can(More)
A method for the identification of direct synaptic connections in a larger neural net is presented. It is based on a conditional correlation graph for multivariate point processes. The connections are identified via the partial spectral coherence of two neurons, given all others. It is shown how these coherences can be calculated by inversion of the(More)
Graphical models applying partial coherence to multivariate time series are a powerful tool to distinguish direct and indirect interdependencies in multivariate linear systems. We carry over the concept of graphical models and partialization analysis to phase signals of nonlinear synchronizing systems. This procedure leads to the partial phase(More)
In this paper the class of ARCH(∞) models is generalized to the nonstationary class of ARCH(∞) models with time-varying coefficients. For fixed time points, a stationary approximation is given leading to the notation " locally stationary ARCH(∞) process. " The asymptotic properties of weighted quasi-likelihood estimators of time-varying ARCH(p) processes (p(More)
A time-varying empirical spectral process indexed by classes of functions is defined for locally stationary time series. We derive weak convergence in a function space, and prove a maximal exponential inequality and a Glivenko–Cantelli-type convergence result. The results use conditions based on the metric entropy of the index class. In contrast to related(More)
In this paper we propose a recursive online algorithm for estimating the parameters of a time-varying ARCH process. The estimation is done by updating the estimator at time point t − 1 with observations about the time point t to yield an estimator of the parameter at time point t. The sampling properties of this estimator are studied in a non-stationary(More)
Over the last decades more and more attention has been paid to the problem how to fit a parametric model of time series with time-varying parameters. A typical example is given by autoregressive models with time-varying parameters (tvAR processes). We propose a procedure to fit such time-varying models to general nonstationary processes. The estimator is a(More)