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Fonction d'autocorrélation partielle des processus à temps discret non stationnaires et applications

Abstract : This thesis presents the partial autocorrelation function of a nonstationary process and some applications in the spectral-domain and in the periodically correlated processes field. After introducing this function, we show that it caracterizes the second order properties of the process. Its interest is to be easily identifiable by comparison with the classical autocovariance function which must be nonnegative definite. Furthermore, it allows us in a natural way to define a new time-dependent power spectrum. At each time, this spectrum describes a stationary situation in which the present is correlated with the past in the same way as our nonstationary process at this time. The study of its properties allows to compare it with two other similar spectra. Next we limit ourselves to the particular class of periodically correlated processes. The partial autocorrelation function get rise to a new parametrization wich gives in particular a natural way to extend the maximum entropy method to this situation. Finally, we consider the autoregressive estimation in this field by proposing an appropriate estimation of these parameters. The comparison with other methods is made by fitting some of them in a general framework and by simulation. We consider also the relation between these approaches and the one associated with the multivariate stationary processes.
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Submitted on : Thursday, February 19, 2004 - 3:04:08 PM
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  • HAL Id : tel-00004893, version 1

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Sophie Lambert-Lacroix. Fonction d'autocorrélation partielle des processus à temps discret non stationnaires et applications. Modélisation et simulation. Université Joseph-Fourier - Grenoble I, 1998. Français. ⟨tel-00004893⟩

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