On prediction intervals for conditionally heteroscedastic processes (Q2784958)
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scientific article; zbMATH DE number 1733177
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On prediction intervals for conditionally heteroscedastic processes |
scientific article; zbMATH DE number 1733177 |
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24 April 2002
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stationary Markov bilinear process
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prediction interval expected length
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0.9123114
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0.8928544
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0.8808246
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0.88029563
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0.87840986
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On prediction intervals for conditionally heteroscedastic processes (English)
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A stationary bilinear process \(X_t=a X_{t-1}+b \varepsilon_t X_{t-1}+\varepsilon_t\) with i.i.d. \(\varepsilon_t\sim N(0,\sigma^2)\) is considered. A standard 95\% prediction interval for \(X_{n+1}\) by \(X_t\), \(t<n\), is NEWLINE\[NEWLINEI=[a X_n-c|1+bX_n|\sigma , a X_n+c|1+bX_n|\sigma],NEWLINE\]NEWLINE where \(c=\Phi^{-1}(0.975)\). The authors demonstrate that the interval NEWLINE\[NEWLINEJ=[a X_n-f(|1+bX_n|)\sigma , a X_n+f(|1+bX_n|)\sigma]NEWLINE\]NEWLINE for some specified function \(f\) is also a 95\% prediction interval for \(X_{n+1}\) and has less unconditional expected length than \(I\).
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