Model-free one-step-ahead prediction intervals: Asymptotic theory and small sample simulations. (English) Zbl 0627.62095

Cho, Sinsup; Miller, Robert B.

Ann. Stat. 15, 1064-1078 (1987).

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.

MSC:

62M20	Inference from stochastic processes and prediction
62G30	Order statistics; empirical distribution functions
60F05	Central limit and other weak theorems

Keywords:

empirical quantile process; ARMA(1,q) process; strongly mixing; double exponential; Gaussian process; model-free one-step-ahead prediction intervals; Simulations; small samples