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

TL;DR

This paper introduces a self-normalized method for constructing confidence intervals in stationary time series that avoids variance estimation and tuning parameters, offering simplicity and broad applicability.

Contribution

It presents a novel, distribution-free self-normalized approach for confidence interval construction that is easy to implement and does not require choosing smoothing parameters.

Findings

Method performs well in finite samples compared to bootstrap.

Theoretical validity established for a broad class of statistics.

Approach is simple, practical, and tuning-parameter free.

Abstract

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 choosing 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 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.