The Annals of Statistics

Adaptive Prediction by Least Squares Predictors in Stochastic Regression Models with Applications to Time Series

C. Z. Wei

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 15, Number 4 (1987), 1667-1682.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350617

Digital Object Identifier
doi:10.1214/aos/1176350617

Mathematical Reviews number (MathSciNet)
MR913581

Zentralblatt MATH identifier
0643.62058

JSTOR
links.jstor.org

Subjects
Primary: 62J05: Linear regression
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62M20: Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11]

Keywords
Adaptive prediction least squares stochastic regression nonstationary autoregressive models order selection

Citation

Wei, C. Z. Adaptive Prediction by Least Squares Predictors in Stochastic Regression Models with Applications to Time Series. Ann. Statist. 15 (1987), no. 4, 1667--1682. doi:10.1214/aos/1176350617. https://projecteuclid.org/euclid.aos/1176350617


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