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

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Abstract:

Summary. 

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.

Keywords: Block bootstrap; Confidence interval; Recursive estimate; Self-normalization; Spectral mean

Document Type: Research Article

DOI: http://dx.doi.org/10.1111/j.1467-9868.2009.00737.x

Affiliations: University of Illinois at Urbana–Champaign, Champaign, USA

Publication date: June 1, 2010

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