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In this paper (1), on page 14 , the authors state "Of special interest in this application is the dependence between the two commodities, once the effect of time has been filtered out".

What do the authors mean with "once the effect of time has been filtered out"?

Does it mean that I cannot use the raw time series values in order to estimate the copula? Do I have to use the residuals?

Would you have some reference that gives a step by step on how to do this copula estimation procedure for time series? As an alternative, could you detail the steps that the author followed in order to get figure 7 from the raw time series data?

(1): Christian Genest, Esterina Masiello, Karine Tribouley. Estimating copula densities through wavelets. Insurance: Mathematics and Economics, Elsevier, 2009, 44 (2), pp.170-181. <10.1016/j.insmatheco.2008.07.006>.

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