Adaptive prediction by least squares predictors in stochastic regression models with applications to time series (Q1102060)
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scientific article; zbMATH DE number 4048893
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Adaptive prediction by least squares predictors in stochastic regression models with applications to time series |
scientific article; zbMATH DE number 4048893 |
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Adaptive prediction by least squares predictors in stochastic regression models with applications to time series (English)
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1987
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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.
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adaptive prediction
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martingale difference sequence
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least squares predictors
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stochastic regression model
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accumulated cost function
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nonstationary autoregressive time series
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