Wavelet Transform Based Multifractal Formalism in Outlier Detection and Localisation for Financial Time Series

We present a method of detecting and localising outliers in financial time series and other stochastic processes. The method checks the internal consistency of the scaling behaviour of the process within the paradigm of the multifractal spectrum. Deviation from the expected spectrum is interpreted as the potential presence of outliers. The detection part of the method is then supplemented by the localisation analysis part, using the local scaling properties of the time series. Localised outliers can then be removed one by one, with the possibility of dynamic verification of spectral properties. Both the multifractal spectrum formalism and the local scaling properties of the time series are implemented on the wavelet transform modulus maxima tree.