Adaptive prediction by least squares predictors in stochastic regression models with applications to time series. (English) Zbl 0643.62058

Wei, C. Z.

Ann. Stat. 15, 1667-1682 (1987).

The asymptotic performance of the least squares predictors \(\hat y_ n\) of the stochastic regression model \(y_ n=\beta_ 1x_{n1}+...+\beta_ px_{np}+\epsilon_ n\) is considered. In particular, the accumulated cost function \(\sum^{n}_{k=1}(y_ k-\hat y_ k-\epsilon_ k)^ 2\) 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.

Reviewer: J.Lillestøl

MSC:

62M20	Inference from stochastic processes and prediction
62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
62J05	Linear regression; mixed models

Keywords:

adaptive prediction; martingale difference sequence; least squares predictors; stochastic regression model; accumulated cost function; nonstationary autoregressive time series