# [R-SIG-Finance] Estimating gumbel copula parameter

Mon Jun 6 01:38:58 CEST 2016

```Hi all. I'm a R newbie, so please bear with me.

I'm fitting nine log losses series (log returns multiplied by -1, so that I have losses on the right and returns on the left) using copulas. My project in more detail:
1) I've filtered the residuals using univariate ARMA-GARCH models, and standardized them dividing by sigma, so that now I have standardized residuals with mean 0 and variance 1 (rugarch package).
2) I modeled the residuals using the generalized pareto distribution family, for all nine series I'm using upper and lower thresholds equal to 0.95 and 0.05 quantiles respectively (spd package).
3) After turning the standardized residuals to their uniform margins using pspd, I'm fitting a Gumbel copula which has upper tail dependence since I'm focusing on losses which are on the right (copula package).
Next part of the work: i) I want to estimate a time-varying Gumbel parameter; ii) given predicted parameter, simulate copula realizations; iii) using the inverse marginal distributions, turn these realizations into standardized residuals; iv) compute returns using ARMA-GARCH specification, convert into simple returns, compute return of equally weighted portfolio and estimate/backtest value at risk and expected shortfall.

Being done with first 2 steps, now I want to estimate a time varying Gumbel. So I'm trying to extract the parameter with a moving window of 500 observations to get an idea of how the time series looks like.

My code looks like this:
theta <- c()
for (i in 1:3345)
{
theta[i]=summary(fitCopula(gumbel.cop,standardized[i:(i+499),], method="ml"))\$coefficients[1]
}

where standardized is a matrix with 9 columns, each with the uniform margin between 0 and 1. So I want to estimate 3345 theta using a window of 500 observations, from theta_1 (obs. 1 to 500) to theta_3345 (obs. 3345 to 4344). However, while running this code, I get:

Error in optim(start, loglikCopula, lower = lower, upper = upper, method = method,  :
valore iniziale in 'vmmin' non finito

where the last sentence can be translated with "initial value in "vmmin" not finite".

What is this error due to? How can I fix this in the command? It runs for the first 1339 estimates (which I've obtained), but from i=1340 this message shows up and I have NA as estimated value.

Any help is appreciated. Thanks.

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