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I want to use a set of daily water quality data including 3 parameters in a Copula model. Somebody told me these data do not have a condition of a random variable to use in copula, and I should do some work on it (my guess is that it involves detrending the data).

Can anybody help me in finding methods to prepare the data to use in a copula method? I would appreciate if you can refer me to good journal papers or books.

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Copulas are used for constructing joint distributions given the marginals. The parameters of the copula are used to model dependencies(correlation) between the marginals.

A good manuscript describing copulas is

http://www.math.uni-leipzig.de/~tschmidt/TSchmidt_Copulas.pdf

Unless you have some reason for transforming the observations from the marginals (maybe scaling or translating them), you do not need to "prepare" them to model them using a copula but maybe you have to take some time to choose properly the corresponding marginal distributions.

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  • $\begingroup$ Thank you for the reply, but my data is a daily water quality data and it it has trend and seasonality therefore it can not be used directly in a copula model. I am sure about that because an expert told me that it is not a random data (I guess it is because that for different days of a year it has a trend). I want to know how can I prepare it to use in the model (I know it can be done by time series analysis and residuals but I don't know how). $\endgroup$
    – Fred
    Commented Dec 7, 2012 at 20:34
  • $\begingroup$ If the data are not random (according to that expert), then you cannot assign a stochastic model. My guess is that you need a different thing. Something like a nonlinear regression model or a time series. But more information about your data would help. $\endgroup$
    – Caesar
    Commented Dec 7, 2012 at 20:56
  • $\begingroup$ I attached the graph of my data (daily values of DO and T for 365 days of the year) in this link tinypic.com/r/2elyqrm/6 $\endgroup$
    – Fred
    Commented Dec 7, 2012 at 21:34
  • $\begingroup$ Regarding the second plot, it looks like a "seasonal trend" with a small variability between two consecutive days. Which is something expected but you can observe some small "noise". See for example the following simulation in R plot(25*sin(seq(1,365,1)*pi/365)+rnorm(365,0,1)). In the first plot the variability between two consecutive days is more apparent. Again, my guess is that what you need here is a nonlinear model that accounts for seasonality and other features present in your context. However, I do think that the data can be treated as random. $\endgroup$
    – Caesar
    Commented Dec 8, 2012 at 0:09

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