IMPROVED SIZER FOR TIME SERIES

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.