Resumen
SiZer (SIgnificant ZERo crossing of the derivatives) is a scale-space visualization tool for statistical inferences. In this paper we introduce a graphical device, which is based on SiZer, for the test of the equality of the mean of two time series. The estimation of the quantile in a confidence interval is theoretically justified by advanced distribution theory. The extension of the proposed method to the comparison of more than two time series is also done using residual analysis. A broad numerical study is conducted to demonstrate the sample performance of the proposed tool. In addition, asymptotic properties of SiZer for the comparison of two time series are investigated.

Resumen
In a random design nonparametric regression model, this paper deals with the detection of a sharp change point and the estimation of a regression function with a single jump point. A method based on design transformation and binning is used in order to convert a random design into an equispaced design whose number of points is a power of 2. Using the continuous wavelet transform of the data, we construct a sharp change point estimator and obtain its rate of convergence. Wavelet methods are well known for their good adaptivity around sudden local changes; however, in practice, the Gibbs phenomenon still exists. This difficulty is overcome by suitably adjusting the data with preliminary estimators for the location and the size of discontinuity. Global and local asymptotic results of the proposed method are obtained. The method is also tested on simulated examples and the results show that the proposed method alleviates the Gibbs phenomenon.