Detection of Outliers of Financial Time Series Based on Wavelet Transform Modulus Maximum

the financial time series is characterized by low SNR, non-stationary, nonlinear. And wavelet transform can highlight the localization of the signal in the time and frequency domain at the same time. So it has the unique advantage of detecting the outliers of the financial time series through using the wavelet transform which is a self-adaptive time-frequency multi resolution analisis method. As all we know, there is a traditional detection of singularity method called Fourier transform which can not accurately comfirm the location of the outliers and the strength of singularity of the signal. But the wavelet transform can better analyse the location of outliers and the strength of singularity. According to the uncertainty principle, it is feasibility and effectiveness to detect the outliers of the financial time series by using the wavelet transform modulus maximum method. We can locate the outliers through tracking the wavelet transform modulus maximum on the smallest scale.