Dealing with Outliers in ARMA Time Series Analysis Using Hampel Filter and Wavelet Analysis

Outliers affect the accuracy of the estimated parameters of ARMA time series models which can be handled by the Hampel filter. In this article, wavelet shrinkage is proposed to handle outliers of ARMA models by using wavelet (Daubechies for order 4, Symlets for order 1, and Dmey) with a universal threshold method and applying a soft threshold. To compare the efficiency of the proposed method and the traditional method (Hampel filter), the mean square error, Akaike and Bayes information criteria were calculated for simulated and real data (The wind speed series data). The proposed method addresses the problem of outliers and provides estimated parameters for ARMA models with higher efficiency than the traditional method.