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

By Xiaofeng Shao. 2010

165 citations recorded by the source corpus.

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.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5eb390aa0221f13842734cebf560312a8fb1fe9d

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Citations in the corpus

Testing relevant hypotheses in functional time series via self‐normalization (2018, methodology): “A third method to obtain (asymptotically) pivotal test statistics is the concept of self-normalization, which was introduced in the seminal papers of Shao (2010) for the construction of confidence intervals and Shao and Zhang (2010) for change point analysis.”
Linear Hypothesis Testing in Dense High-Dimensional Linear Models (2016, methodology): “Compared with the existing approaches where the normalization factor is a consistent estimator of the asymptotic variance, our self-normalized approach adopts an inconsistent estimator as the normalization factor, which in a sense corresponds to “ineﬃcient Studentizing” (cf. Shao (2010)).”
Testing the structural stability of temporally dependent functional observations and application to climate projections (2011, methodology): “The idea of using inconsistent normalization is not new, as it has been previously applied by Lobato [16] and Shao [22] to the inference in univariate time series.”
Testing for Change Points in Time Series (2010, methodology): “The basic idea is to extend the selfnormalization (SN) method (Lobato 2001; Shao 2010) to the change-point testing problem.”
Should we go one step further? An accurate comparison of one-step and two-step procedures in a generalized method of moments framework (2018, background): “This includes, among others, Ibragimov and Müller (2010), Shao (2010) and Bester, Conley, and Hansen (2011).”
A simple test of changes in mean in the possible presence of long‐range dependence (2011, methodology): “The self-normalization idea has been used by Lobato (2001) and Shao (2009, 2010) for inference problems related to weakly dependent time series.”
The Cross-Quantilogram: Measuring Quantile Dependence and Testing Directional Predictability between Time Series (2014, unknown): “Shao, X. (2010) A self-normalized approach to confidence interval construction in time series, Journal of the Royal Statistical Society Series B, 72, 343-366. Sun, Y. and M.S. Kim (2012) Simple and powerful GMM over-identification tests with accurate size, Journal of Econometrics, 166, 267-281. Sun,”