Model-Free One-Step-Ahead Prediction Intervals: Asymptotic Theory and Small Sample Simulations
Cho, Sinsup ; Miller, Robert B.
Ann. Statist., Tome 15 (1987) no. 1, p. 1064-1078 / Harvested from Project Euclid
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We show that the empirical quantile process from an ARMA$(1, q)$ process which is strongly mixing $\Delta_s$, and is either Gaussian or double exponential, converges to a Gaussian process. This result is used to derive model-free one-step-ahead prediction intervals for such processes. Simulations demonstrate where the asymptotic theory can and cannot be applied to small samples.
Publié le : 1987-09-14
Classification:  Strong mixing $\Delta_s$,  empirical quantile process,  prediction interval,  62G30,  62M20 
@article{1176350493,
     author = {Cho, Sinsup and Miller, Robert B.},
     title = {Model-Free One-Step-Ahead Prediction Intervals: Asymptotic Theory and Small Sample Simulations},
     journal = {Ann. Statist.},
     volume = {15},
     number = {1},
     year = {1987},
     pages = { 1064-1078},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176350493}
}

Cho, Sinsup; Miller, Robert B. Model-Free One-Step-Ahead Prediction Intervals: Asymptotic Theory and Small Sample Simulations. Ann. Statist., Tome 15 (1987) no. 1, pp.  1064-1078. http://gdmltest.u-ga.fr/item/1176350493/