For the class of stationary Gaussian long memory processes, we study some properties of the leastsquares predictor of X n+1 based on (X n , . . . , X 1 ). The predictor is obtained by projecting X n+1 onto the finite past and the coefficients of the predictor are estimated on the same realisation. First we prove moment bounds for the inverse of the empirical covariance matrix. Then we deduce an asymptotic expression of the mean-squared error. In particular we give a relation between the number of terms used to estimate the coefficients and the number of past terms used for prediction, which ensures the L 2 -sense convergence of the predictor. Finally we prove a central limit theorem when our predictor converges to the best linear predictor based on all the past.
Abstract. We present two approaches for linear prediction of long-memory time series. The first approach consists in truncating the Wiener-Kolmogorov predictor by restricting the observations to the last k terms, which are the only available data in practice. We derive the asymptotic behaviour of the mean-squared error as k tends to +∞. The second predictor is the finite linear least-squares predictor i.e. the projection of the forecast value on the last k observations. It is shown that these two predictors converge to the Wiener Kolmogorov predictor at the same rate k −1 .
Certains facteurs démographiques, économiques et financiers sont susceptibles d’avoir de fortes répercussions sur les futures pensions de réversion. Cet article propose d’évaluer, à l’aide du modèle de microsimulation Destinie, développé à l’Insee, la sensibilité de la réversion à la réduction des écarts genrés d’espérance de vie, à la convergence des trajectoires professionnelles féminines et masculines, ou encore à des variantes (paramétriques ou systémiques) du dispositif actuel. Ainsi, la généralisation de la condition de ressources qui prévaut actuellement pour le régime général créerait des économies pour les caisses de retraite tout en étant redistributive. Une logique d’« assurance veuvage », qui viserait à maintenir le niveau de vie au moment du décès du conjoint, générerait des « gagnants » et des « perdants », avec un effet redistributif globalement neutre.
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