A modified wavelet-based method for detection of outliers in time series

As a multi-resolution analysis, wavelet transformation tool has been used to detect contingent outliers in time series data with no need to specify a model for the data. The objective of this article is to design an orthonormal wavelet system that optimizes the wavelet-based outlier detection procedure. In addition, we show that regardless of the selected base functions, the existing wavelet-based methods extract two adjacent suspicious observations so that probably one of them is an outlier. Therefore, we modify the wavelet-based outlier detection scheme by introducing a transformation matrix consisting of our designed wavelet filters that can be used to detect outlying observations without the above-mentioned ambiguity. In a numerical example, a sample observation vector is analyzed using our scheme. At the same time, a robust statistical approach- modified z-score method- has been used to evaluate the capability of our desired wavelet-based procedure. The results were completely reliable and comparable.