Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1149308 | Journal of Statistical Planning and Inference | 2010 | 20 Pages |
Abstract
For the class of stationary Gaussian long memory processes, we study some properties of the least-squares predictor of Xn+1 based on (Xn,â¦,X1). The predictor is obtained by projecting Xn+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 L2- 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Fanny Godet,