Optimiation Wavelet Thresholding in Non-Stationary Time-Series Analysis for Treatments Tuberculosis Case Patients Optimiation Wavelet Thresholding in Non-Stationary Time-Series Analysis for Treatments Tuberculosis Case Patients

Abstract

Abstract: Non-stationary time series (TS) analysis has gained great interest over the last few decades in various applied sciences. In fact, several decomposition methods were developed to extract various components (e.g., seasonal, trend, and sudden components) from non-stationary TS, which allows a better interpretation of temporal variability. Wavelet Thresholding (WT) has been successfully applied over a tremendous range of fields to decompose non-stationary TS into the time-frequency domain. There are two types of wavelet estimators, namely linear wavelet estimators and nonlinear wavelet estimators. Linear wavelet estimators can be analyzed using the Multiresolution Analysis (MRA) approach, while nonlinear wavelet estimators are called Wavelet Thresholding (WT). Wavelet Thresholding emphasizes wavelet reconstruction using the largest number of coefficients or you could say only coefficients that are greater than the value taken, while other coefficients are ignored. There are various challenges for optimization related to wavelet transform, such as selecting the type of wavelet, selecting an adequate parent wavelet, selecting the scale, combining wavelet transform and machine learning algorithms. Apart from that, there are several factors that influence the smoothness of the estimation, namely the type of wavelet function, type of threshold function, threshold parameters, and level of resolution. Therefore, in this paper the optimal threshold value will be obtained in analyzing the data. The Wavelet Thresholding method provides a smaller MSE, MAPE, SNR and Energy value compared to the wavelet method with the Multiresolution Analysis (MRA) approach. In this case study, Wavelet Thresholding is considered better in time series data analysis.

Keywords : Wavelet Thresholding Estimator, Multiresolution Analysis, Tunning Parameter, Non stationary