[R-SIG-Finance] Dynamic copula simulation with 'rmgarch' package
Sachin Kuruvithadam
sacios at hotmail.it
Fri Jun 10 12:44:19 CEST 2016
Hi, I have 2 questions about GARCH-SPD-copula fitting.
I'm using a time-varying normal copula with DCC dynamics of the correlation structure. I use the semiparametric distribution with generalized pareto distribution, which is specified in 'cgarchspec' and controlled for in 'cgarchfit' (with thresholds at 0.05 and 0.95). After running the code similar to the example in 'rmgarch.tests' folder (adjusted for my ARMA-GARCH specification and data), 'simX[[i]]' is a Nxd matrix (N=steps ahead, d=number of assets) containing all conditional returns of the i-th simulation.
My questions:
A) Is it possible to extract the GPD parameters in this procedure, maybe from the 'cgarchfit' object, or am I supposed to estimate xi and beta separately through the 'spd' package? In this case, are these estimates the same used in the 'rmgarch' package?
B) Are the conditional returns in 'simX[[i]]' already controlled for the copula and SPD specification? i.e. are they computed following the procedure: i) given data at t, construct correlation matrix at t+1; ii) generate the (1xd) vector of correlated copula realizations m times; iii) using the inverse of the SPD obtain standardized residuals; iv) insert the latter back in the ARMA-GARCH specification and compute returns; v) repeat steps i-iv until the end of the simulation horizon?
Intuitively I would say yes to both questions, i.e. the GPD parameters used in 'rmgarch' and 'spd' are the same if they are specified the same (thresholds at 0.05 and 0.95, mle with normal kernel) and 'simX[[i]]' already runs the whole procedure mentioned above, i.e. simulates copula realizations, converts them into original realizations using the inverse CDF and feeds them in the respective ARMA-GARCH process (otherwise why do we specify the ARMA-GARCH for each series, the copula family and the transformation in 'cgarchspec' with thresholds in 'cgarchfit'?) but I've found no "official" confirmation.
Thank you in advance.
sacios
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