Hello everybody, I'm pretty new to R and copulas and I have a few questions
I need to clarify, hope someone here can help me out. 

It's basic stuff. 

 

Start with the following simple setting. 

 

-I want to estimate Archm copulas from bivariate data: (weekly) returns of
Swiss Market Index SMI and German Stock Index DAX: I use approx 985 weeks,
i.e. 985 data pairs 

-I calculate the empirical dist function using ranks in excel and feed this
data series into R (there should be a more efficient way to do this, no,
it's quite repetitive to do this over again in excel.)

-enter the following code (example)  

 

>fitCopula(claytonCopula, full.u, method="ml"); full.u is the name of the
data frame, clayton.cop has been specified before appropriately.

 

-result: 

 

>fitCopula(clayton.cop, full.u, method = "ml")

The estimation is based on the maximum likelihood

and a sample of size 985.

 Estimate Std. Error  z value Pr(>|z|)

param 1.636907 0.07953911 20.57990        0

The maximized loglikelihood is  333.3923 

The convergence code is  0  

 

.         QUESTIONs: Is this the standard way to tackle problems like this?
If so, why is the result so different when I use method="itau"? It is:
2.095738  parameter value.  

.          What do the numbers after the parameter mean? Is this a test of
the hypothesis that the parameter is zero? Is  Pr(>|z|) some kind of
p-value? 

.         There seems to be no big difference between method="mpl " and
method="ml". Can somebody explain the difference and especially when I
should use which of the two commands..?  but pls don't tell me to read the
Copula package manual, I have done this.) 

 

The second thing I do now it to test the results I have gotten above. Stick
with the example. 

 

Enter the code:

> gofCopula(claytonCopula(2.095738), full.u, 500) 

-result: 

> Parameter estimate(s): 1.639066 

Cramer-von Mises statistic: 0.2790018 with p-value 0.000998004

 

-When I test the gumbel copula on the same data set, I get

 

> Parameter estimate(s): 1.989039 

Cramer-von Mises statistic: 0.1135297 with p-value 0.000998004

 

.which is weird since I get the EXACT same p-value as when I tested the
clayton copula!! Is this correct or is there a bug? 

 

 

.         (More) QUESTIONs: It seems that gofCopula kind of re-caculates the
parameter value: why do you need the fitCopula command in the first place? 

.         What does this result mean for clayton and gumbel? It seems to be
pretty bad since the p-value is small. One would thus say that the Null is
rejected and hence reject the model for the data set.

.         .which leads me to the most important question: The way I have
done this procedure so far, is this appropriate for this kind of task
(estimate copulas from index return data) or am I completely on the wrong
track here? I mean, can I say now: "According to my estimation an testing,
the Clayton copula should not be used to model the returns of SMI and DAX"? 

 

I don't want this first post too packed, so this should wrap it up for the
time being. Would be GREAT if someone could help me out here., help much
much appreciated.

Thanks you, Michael


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