Generalization of the cross-wavelet function

Herrera, Víctor Manuel Velasco; Soon, Willie; Herrera, Graciela Velasco; Horiuchi, Kazuho

doi:10.1016/j.newast.2017.04.012

Cited by 22 publications

(20 citation statements)

References 19 publications

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“…For example, Soon et al [89] used the multiple cross-wavelet transform algorithm to analyze the Holocene solar and climatic variations. Then, Herrera et al [90] developed a generalisation of the XWT in order to study the solar activity records. In addition, Aguiar-Conraria and Soares [91] used the multivariate version of the CWT and Fernández-Macho [83] investigated the extended (multivariate version) version of the wavelet correlation via MODWT in order to analyze the correlation between financial time series.…”

Section: Discussionmentioning

confidence: 99%

Wavelet Transform Application for/in Non-Stationary Time-Series Analysis: A Review

et al. 2019

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Non-stationary time series (TS) analysis has gained an explosive interest over the recent decades in different applied sciences. In fact, several decomposition methods were developed in order to extract various components (e.g., seasonal, trend and abrupt components) from the non-stationary TS, which allows for an improved interpretation of the temporal variability. The wavelet transform (WT) has been successfully applied over an extraordinary range of fields in order to decompose the non-stationary TS into time-frequency domain. For this reason, the WT method is briefly introduced and reviewed in this paper. In addition, this latter includes different research and applications of the WT to non-stationary TS in seven different applied sciences fields, namely the geo-sciences and geophysics, remote sensing in vegetation analysis, engineering, hydrology, finance, medicine, and other fields, such as ecology, renewable energy, chemistry and history. Finally, five challenges and future works, such as the selection of the type of wavelet, selection of the adequate mother wavelet, selection of the scale, the combination between wavelet transform and machine learning algorithm and the interpretation of the obtained components, are also discussed.

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Section: Discussionmentioning

confidence: 99%

Wavelet Transform Application for/in Non-Stationary Time-Series Analysis: A Review

et al. 2019

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“…Another famous data set is presented in [12] as an application to biology, by studying the growth of children as a time continuous phenomenon. Those works and data sets are today considered as benchmarks to test new methods, but many fields such as economy [13], energy [14], medicine [15] or astronomy [16] have used FDA and contribute to this really active research topic.…”

Section: Longitudinal Data In Sportmentioning

confidence: 99%

Functional Data Analysis in Sport Science: Example of Swimmers’ Progression Curves Clustering

et al. 2018

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Many data collected in sport science come from time dependent phenomenon. This article focuses on Functional Data Analysis (FDA), which study longitudinal data by modelling them as continuous functions. After a brief review of several FDA methods, some useful practical tools such as Functional Principal Component Analysis (FPCA) or functional clustering algorithms are presented and compared on simulated data. Finally, the problem of the detection of promising young swimmers is addressed through a curve clustering procedure on a real data set of performance progression curves. This study reveals that the fastest improvement of young swimmers generally appears before 16 years old. Moreover, several patterns of improvement are identified and the functional clustering procedure provides a useful detection tool.

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“…Specifically, "→" denotes that the variations of factors 2 and 1 are synchronous, "↓" indicates that the variation of factor 2 lags behind that of factor 1 with one-fourth of an RP, "←" implies that the variation of factor 2 lags behind that of factor 1 with half of an RP, and "↑" shows that the variation of factor 2 lags behind that of factor 1 with three-fourths of an RP. Additional information about wavelet cross spectra was given by Herrera et al [56].…”

Section: Correlations Between Tws and Climatic And Vegetational Factorsmentioning

confidence: 99%

GRACE-Based Terrestrial Water Storage in Northwest China: Changes and Causes

et al. 2018

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Monitoring variations in terrestrial water storage (TWS) is of great significance for the management of water resources. However, it remains a challenge to continuously monitor TWS variations using in situ observations and hydrological models because of a limited number of gauge stations and the complicated spatial distribution characteristics of TWS. In contrast, the Gravity Recovery and Climate Experiment (GRACE) could overcome the aforementioned restrictions, providing a new reliable means of observing TWS variation. Thus, GRACE was employed to investigate TWS variations in Northwest China (NWC) between April 2002 and March 2016. Unlike previous studies, we focused on the interactions of multiple climatic and vegetational factors, and their combined effects on TWS variation. In addition, we also analyzed the relationship between TWS variations and socioeconomic water consumption. The results indicated that (i) TWS had obvious seasonal variations in NWC, and showed significant decreasing trends in most parts of NWC at the 95% confidence level; (ii) decreasing sunshine duration and wind speed resulted in an increase in TWS in Qinghai province, whereas the increasing air temperature, ameliorative vegetational coverage, and excessive groundwater withdrawal jointly led to a decrease in TWS in the other provinces of NWC; (iii) TWS variations in NWC had a good correlation with water storage variations in cascade reservoirs of the upper Yellow River; and (iv) the overall interactions between multiple climatic and vegetational factors were obvious, and the strong effects of some climatic and vegetational factors could mask the weak influences of other factors in TWS variations in NWC. Hence, it is necessary to focus on the interactions of multiple factors and their combined effects on TWS variations when exploring the causes of TWS variations.

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Generalization of the cross-wavelet function

Cited by 22 publications

References 19 publications

Wavelet Transform Application for/in Non-Stationary Time-Series Analysis: A Review

Wavelet Transform Application for/in Non-Stationary Time-Series Analysis: A Review

Functional Data Analysis in Sport Science: Example of Swimmers’ Progression Curves Clustering

GRACE-Based Terrestrial Water Storage in Northwest China: Changes and Causes

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