Wavelet-based Detection Of Outliers In Time Series

In this paper, we first give a fully review on the detection of outliers in data, and introduce several standard outlier detection methods, such as method based on dis-tance, method based on density and so on. At the same time, we introduce continuous wavelet and discrete wavelet transform, we combine DWT with outlier detection in time series, put forward the new method to design threshold of the outlier detection, and based on this we put forward the wavelet-based detection of outliers in ARFIMA model. We choose AR, MA, ARM A models and do some simulation studies. The results show good performance of the proposed method.For real data analysis, we investigate the Shanghai Composite Index and the Shenzhen Component Index respectively, and fit the data of stock market by using low-order ARFIMA model, and detect outliers based on residuals of the data. At the same time, we compare it with low-order GARCH model, and get the conclusion that the ARFIMA model has more advantage on detection of outliers in stock market, because the data in stock market have long memory property.