TESTING FOR OUTLIERS IN TIME SERIES USING WAVELETS

One remarkable feature of wavelet decomposition is that the wavelet coefficientsare localized, and any singularity in the input signals can only affect the wavelet coefficientsat the point near the singularity The localized property of the wavelet coefficients allowsus to identify the singularities in the input signals by studying the wavelet coefficients atdifferent resolution levels. This paper considers wavelet-based approaches for the detectionof outliers in time series. Outliers are high-frequency phenomena which are associated withthe wavelet coefficients with large absolute values at different resolution levels. On the basisof the first-level wavelet coefficients, this paper presents a diagnostic to identify outliers ina time series. Under the null hypothesis that there is no outlier, the proposed diagnosticis distributed as a X~2. Empirical examples are presented to demonstrate the applicationof the proposed diagnostic.