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Statistica Sinica 19 (2009), 1511-1530


Cheolwoo Park, Jan Hannig and Kee-Hoon Kang

University of Georgia, University of North Carolina at Chapel Hill
and Hankuk University of Foreign Studies

Abstract: SiZer (SIgnificant ZERo crossing of the derivatives) is a scale-space visualization tool for statistical inferences. In this paper we improve global inference of SiZer for time series, originally proposed by Rondonotti, Marron and Park (2007), in two aspects. First, the estimation of the quantile in a confidence interval is theoretically justified by advanced distribution theory. Second, an improved nonparametric autocovariance function estimator is proposed using a differenced time series. A numerical study is conducted to demonstrate the sample performance of the proposed tool. In addition, asymptotic properties of SiZer for time series are investigated.

Key words and phrases: Autocovariance function estimation, local linear smoothing, multiple testing adjustment, SiZer, statistical convergence, time series.

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