Estimation and Prediction in Gegenbauer processes: application to traffic data.
Author: Dominique Guegan
In this talk we present the long memory Gegenbauer process which allow to take into
account the periodic behavior of a time series with long range dependance. We investigate
the speudo maximun likehood Whittle 's method to estimate simultaneously all the
parameters of the Gegenbauer model. We provide a result of asymptotic convergence for the
Whittle's estimator and use Monte Carlo simulations to validate our result. Then we
compute the analytical expression of the prediction function when the parameters are known
or unknown . We precise the confidence intervals.
We propose an application to data of urban transport traffic, which points out the
efficiency of the Gegenbauer model, especially in the long term forecasting domain.
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