Journal Article

A self-normalized approach to confidence interval construction in time series

Shao, Xiaofeng

2010

Overview

We propose a new method to construct confidence intervals for quantities that are associated with a stationary time series, which avoids direct estimation of the asymptotic variances. Unlike the existing tuning-parameter-dependent approaches, our method has the attractive convenience of being free of any user-chosen number or smoothing parameter. The interval is constructed on the basis of an asymptotically distribution-free self-normalized statistic, in which the normalizing matrix is computed by using recursive estimates. Under mild conditions, we establish the theoretical validity of our method for a broad class of statistics that are functionals of the empirical distribution of fixed or growing dimension. From a practical point of view, our method is conceptually simple, easy to implement and can be readily used by the practitioner. Monte Carlo simulations are conducted to compare the finite sample performance of the new method with those delivered by the normal approximation and the block bootstrap approach.

• Publisher: Blackwell Publishing Ltd,Wiley-Blackwell,Blackwell,Royal Statistical Society,Oxford University Press
• Subject: Approximation / Asymptotic properties / Block bootstrap / Bootstrap mechanism / Bootstrap method / Computer simulation / Confidence / Confidence interval / Confidence intervals / Consistent estimators / Construction / Distribution / Estimates / Estimation / Estimators / Exact sciences and technology / General topics / Inference from stochastic processes; time series analysis / Interval estimators / Interval scale / Mathematical analysis / Mathematics / Methodology / Monte Carlo method / Monte Carlo methods / Nonparametric inference / Parametric inference / Point of view / Probability and statistics / Recursion / Recursive algorithms / Recursive estimate / Sample size / Samples / Sciences and techniques of general use / Scientific method / Self-normalization / Simulation / Smoothing / Spectral mean / Statistical discrepancies / Statistics / Stochastic processes / Studies / Time series / time series analysis / Time series models