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December, 1987 Adaptive Prediction by Least Squares Predictors in Stochastic Regression Models with Applications to Time Series
C. Z. Wei
Ann. Statist. 15(4): 1667-1682 (December, 1987). DOI: 10.1214/aos/1176350617

Abstract

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.

Citation

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C. Z. Wei. "Adaptive Prediction by Least Squares Predictors in Stochastic Regression Models with Applications to Time Series." Ann. Statist. 15 (4) 1667 - 1682, December, 1987. https://doi.org/10.1214/aos/1176350617

Information

Published: December, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0643.62058
MathSciNet: MR913581
Digital Object Identifier: 10.1214/aos/1176350617

Subjects:
Primary: 62J05
Secondary: 62M10, 62M20

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 4 • December, 1987
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