Herein we consider the asymptotic performance of the least squares predictors $\hat{y}_n$ of the stochastic regression model $y_n = \beta_1 x_{n1} + \cdots + \beta_p x_{np} + \varepsilon_n$. In particular, the accumulated cost function $\sum^n_{k=1} (y_k - \hat{y}_k - \varepsilon_k)^2$ is studied. The results are then applied to nonstationary autoregressive time series. A statistic is also constructed to show how many times one should difference a nonstationary time series in order to obtain a stationary series.
Publié le : 1987-12-14
Classification:
Adaptive prediction,
least squares,
stochastic regression,
nonstationary autoregressive models,
order selection,
62J05,
62M10,
62M20
@article{1176350617,
author = {Wei, C. Z.},
title = {Adaptive Prediction by Least Squares Predictors in Stochastic Regression Models with Applications to Time Series},
journal = {Ann. Statist.},
volume = {15},
number = {1},
year = {1987},
pages = { 1667-1682},
language = {en},
url = {http://dml.mathdoc.fr/item/1176350617}
}
Wei, C. Z. Adaptive Prediction by Least Squares Predictors in Stochastic Regression Models with Applications to Time Series. Ann. Statist., Tome 15 (1987) no. 1, pp. 1667-1682. http://gdmltest.u-ga.fr/item/1176350617/