Wavelet Methods For Time Series Analysis Percival Pdf 25
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This analysis provides evidence regarding the timely and appropriate measure of correlation changes and the behaviour of sukuk and bond indices globally, which is beneficial to the management of sukuk and bond portfolios.
Bhuiyan, R.A., Rahman, M.P., Saiti, B. and Mat Ghani, G. (2019), "Co-movement dynamics between global sukuk and bond markets: New insights from a wavelet analysis", International Journal of Emerging Markets, Vol. 14 No. 4, pp. 550-581. -12-2017-0521
Wastewater-based epidemiology (WBE) is a novel approach in drug use epidemiology which aims to monitor the extent of use of various drugs in a community. In this study, we investigate functional principal component analysis (FPCA) as a tool for analysing WBE data and compare it to traditional principal component analysis (PCA) and to wavelet principal component analysis (WPCA) which is more flexible temporally.
We analysed temporal wastewater data from 42 European cities collected daily over one week in March 2013. The main temporal features of ecstasy (MDMA) were extracted using FPCA using both Fourier and B-spline basis functions with three different smoothing parameters, along with PCA and WPCA with different mother wavelets and shrinkage rules. The stability of FPCA was explored through bootstrapping and analysis of sensitivity to missing data.
Recently, functional principal component analysis (FPCA) has been explored as a statistical method for analysing wastewater data . The approach was found not only to be well suited for extracting useful information about the different drug loads during the course of a week, but also extracted detailed information that would otherwise be lost when using more traditional statistical methods. It can easily be argued that functional data analysis (FDA) is a reasonable approach to analysing temporal wastewater data , but there is a concern that the basis functions of the FDA framework might be too smooth to model the rapid temporal changes in drug load curves that can occur over the course of a week, especially the change between weekdays and weekend. Alternative, more flexible, statistical approaches should also be explored.
Wavelets have a long tradition in time series analysis . Wavelet basis functions are localized in both frequency and time domains simultaneously, allowing for the extraction of features that are less smooth from temporal data [20, 21]. Wavelet-based principal component analysis (WPCA) has recently been applied successfully to analysis of foetal movement monitoring data [22, 23]. The temporally more flexible WPCA could be able to detect rapid temporal changes in wastewater data.
The unit of observation in the analysis is a seven day week starting Wednesday and ending Tuesday. As wavelet analysis generally requires individual time series to have a length of a power of two observations , we added the first observation to the end of the time series, generating an eight day time series, for ease of comparison. This additional day is needed only for technical purposes and does not have any impact on the results . Missing data across all the 38 cities was 2.2 %. As standard frequentist functional data analysis (FDA) needs complete data sets for analysis, we performed single imputation  using the bootstrapping-based expectation maximization algorithm , before proceeding with the analysis on the imputed dataset. Moreover, the wastewater data was heavily skewed, and the data was log-transformed prior to further analysis.
Using traditional PCA, each day of the week is considered a single variable and each PC resulting from the PCA is defined as a linear combination of the original variables. Since in PCA the load of a drug at a given day is assumed to be independent of the drug load at any other day, be it preceding or following days, the correlation between individual days is not taken into account. This assumption is however likely to be violated for wastewater data where consecu