The Annals of Statistics

Model-Free One-Step-Ahead Prediction Intervals: Asymptotic Theory and Small Sample Simulations

Sinsup Cho and Robert B. Miller

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 15, Number 3 (1987), 1064-1078.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350493

Digital Object Identifier
doi:10.1214/aos/1176350493

Mathematical Reviews number (MathSciNet)
MR902246

Zentralblatt MATH identifier
0627.62095

JSTOR
links.jstor.org

Subjects
Primary: 62G30: Order statistics; empirical distribution functions
Secondary: 62M20: Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11]

Keywords
Strong mixing $\Delta_s$ empirical quantile process prediction interval

Citation

Cho, Sinsup; Miller, Robert B. Model-Free One-Step-Ahead Prediction Intervals: Asymptotic Theory and Small Sample Simulations. Ann. Statist. 15 (1987), no. 3, 1064--1078. doi:10.1214/aos/1176350493. https://projecteuclid.org/euclid.aos/1176350493


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