# Wavelet Transform Application for/in Non-Stationary Time-Series Analysis: A Review
## 4 Discussion
[89] used the multiple cross-wavelet transform algorithm to analyze the Holocene solar and climatic variations. Then, [PERSON] et al. [90] developed a generalisation of the XWT in order to study the solar activity records. In addition, [PERSON] and [PERSON] [91] used the multivariate version of the CWT and [PERSON] [83] investigated the extended (multivariate version) version of the wavelet correlation via MODWT in order to analyze the correlation between financial time series. As a result, WT has proved its effectiveness in the different fields. It can be considered as a noise reduction approach by eliminating the detail components of the first level. In addition, WT extracts more information due to the hierarchical strategy of multiple frequency dynamics within the TS. In fact, different types of WT have been used (e.g., CWT, DWT, stationary WT, EWT, XWT and WPD) and several mother wavelets have been selected (e.g., Meyer, Morlet, Daubechies, Symlet, Haar, Coiflets). This variety and availability of different functions is considered as a key advantage of WT due to the possibility of choosing the most appropriate for the signal under investigation. However,the application of WT has not achieved a standard status yet. The different challenges of wavelet decomposition which were not extensively dealt with in this review will be discussed. * Selection of WT type: First, a general methodology for selecting the adequate WT (DWT, CWT, WPD, MODWT, XWT, WTC, EWT) is still missing. In addition, only some articles, such as [PERSON] et al. [92], discussed the advantages and disadvantages of DWT and CWT. In fact, all the methods have different superiorities. For example, the CWT is superior in determining the scale contents and the variety in time. However, the DWT is well-known for decomposing the series into sub-signals given the proper wavelet and temporal scale. Additionally, the experimental results are principally used in order to choose the adequate wavelet, as introduced in [PERSON] et al. [55] and [PERSON] et al. [48]. * Choice of mother wavelet: The second challenge is the choice of the proper mother wavelet. In fact, the quality of the obtained results is affected by the wavelet function. Generally, a mother wavelet has the following properties, namely orthogonality, compact size, support, symmetry, and vanishing moment [93]. However, the same properties can exist in different mother wavelets. To overcome this drawback, it should be admitted that the choice of wavelet is related to the type of application and the used TS. [PERSON] et al. [92] have proposed that the wavelet properties and the composition of the series are the principal criteria for selecting the adequate mother wavelet. The different properties introduced by [PERSON] are summarized as follows: (1) the wavelet should have the progressive and linear phase; (2) the wavelet should exhibit a good localization both in time and frequency domains; (3) the wavelet should be adapted to the trade-off between time and scale resolutions; and (4) the wavelet should also meet the orthogonal condition. Recently, [PERSON] et al. [94] have used a statistical test in order to compare 38 mother wavelets. The information Quality Ratio has been tested for seven different TS as a new statistical metric for mother wavelet selection. In addition, some other works have also dealt with this empirical problem [31; 47]. * Selection of the timescale: The selection of the range scales used in the WT is an ignored problem. In fact, the scales that are out of range result in meaningless information, thus misleading the signal analysis. [PERSON] et al. [95] have examined the influence of the level of decomposition on the forecasting task. The majority of solutions to this problem are qualitative and empirical. However, objective and operable methods are much more needed. * Combination with machine learning: To our knowledge, the present applications such as forecasting cannot be made using WT alone.