[Statlist] Séminaire Statistique, Université de Neuchâtel le 16/10/2007

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S�minaire de Statistique 
Institut de Statistique, Universit� de Neuch�tel 

Pierre � Mazel 7 (1er �tage,salle 110), Neuch�tel,

http://www2.unine.ch/statistics

Mardi 16 octobre 2007, 11h00

************************

Olivier Renaud, 

Section de Psychologie - FPSE, Universit� de Gen�ve

 

Prediction and State-Space Filtering of Time Series. 

We present a new method for the prediction of time series and for the filtering of processes that are measured with noise (state-space models). It is based on a special (overcomplete) multiscale decomposition of the signal called the � trous wavelet transform. 

 

In the case of prediction, we use this decomposition to fit either a very simple autoregressive model or a more complex neural network. However, virtually any prediction scheme can be adapted to this representation.  Even with the simplest autoregressive model, this method is able to capture short and long memory components of the series in an adaptive and very efficient way and we show in this case the convergence of the method towards the optimal prediction. Simulations show that it can capture fractionnal ARIMA series as well as very short-term dependency series. The number of parameters to be estimated is adative to the sturcture of the series and always stay moderate, but thanks to the multiresolution, the model capture long dependencies. 

 

In the filtering case, the same prediction scheme can be used and we use the multiscale entropy filtering instead of the usual trade-off inherent in the Kalman filter. The entropy method, adapted from the denoising purpose, reveals very powerful in this multiscale framework and has several advantages. It is competitive in the cases where the Kalman filter is known to be optimal, but it is much more useful when the transition equation is not linear any more.  Moreover, the multiscale entropy filtering is robust relative to Gaussianity of the transition noise. 

 


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