# Wavelet Transform Application for/in Non-Stationary Time-Series Analysis: A Review
## 4 Discussion  
Several representative literature sources about the applications of WT in different fields were reviewed above. However, all the publications seem to be virtually impossible to be reviewed. A summary of the WT applications in different fields will be described below, followed by a discussion of the actual challenges and the future perspectives of WT. In geo-sciences and geophysics, different basic wavelet transforms are used such as the DWT, CWT, MODWT and XWT [23; 25; 76]. Principally the WT are used for trend analysis, correlation and coherency between two time series, cross-spectral analysis and wavelet based spatial verification, whereas there are limited applications concerning forecasting. In remote sensing fields, different types of WT were applied, namely CWT, MODWT, DWT-MRA to NDVI and EVI TS. Principally, the MRA-DWT proved its effectiveness in several works [34; 35; 38; 40]. Compared to other methods, [PERSON] et al. [40] proved that WT is faster than the BFAST method and is more informative. To our knowledge, the presented applications of WT in remote sensing in vegetation concentrate on wavelet denoising and multi-scale analysis, whereas there are limited applications concerning trend analysis and forecasting. In hydrology, both DWT and CWT are considered as the mostly used methods. The CWT was especially used to localize non-stationary variability, whereas DWT was used for denoising and the identification of true components. Compared with other statistical methods, WT has the advantage of identifying the nonstationary variability of hydrologic variables at multi-time scales, which is important to understand the hydrologic variability and to make mid-to-long-term predictions. In the future, wavelet de-noising, wavelet-aided complexity description and wavelet cross-correlation analyses should be further investigated in order to understand the hydrologic process. In medicine, WT was used in several applications, such as denoising, compression, frequency analysis and forecasting, in order to analyze the EEG and ECG data. The main advantage of WT in this field is flexibility in the local spectral and temporal information received from a signal. In fact, short duration, high frequency, longer duration, and lower frequency information can be captured simultaneously. Generally, several parameters such as the mother wavelet and the scale are tested in order to improve the performance of the related methods [88]. The choice of one or more parameter is made using different statistical tests, such as MSE, CR and PRD. In addition, several types of WT, such as DWT, EWT, and WPD, were investigated. [PERSON] et al. [64] have recently proved that WPD gives a better performance than DWT. However, the CWT has not been well investigated in this field. A research study on CWT can be conducted to analyze medicine TS and can yield good results in several applications. In finance, the DWT, MODWT and XWT are the principal used types [52; 59], where the main advantage is the ability to conserve time information. Future research prospects in this field will be forecasting the financial behaviour in stock market and study the mitigation of agency cost. In engineering, different data were used for TS denoising, prediction, feature extraction, etc. Several types of wavelets, such as DWT, CWT, and WPD, were tested. In this field, DWT coefficients are particularly useful for signal compression problems, whereas CWT is favoured when a high temporal resolution is required at all scales. Compared to other temporal methods, WT has the ability of multi-scale analysis and time-frequency features extraction. In the future, the analysis of two or more signals simultaneously must be more investigated in order to find the relationship between the different TS. In addition, both in geo-sciences and finance, the wavelet cross-correlation was well investigated. Recently, a multi variate wavelet transform version was developed in order to analyze more than two time series. For example, [PERSON] et al.