Questions tagged [extremal-dependence]
8 questions
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Understanding tail dependence coefficients
How can I analyze the $\lambda_U$ and $\lambda_L$ results (estimated by non-parametric method)? What does higher or lower coefficients mean? Does $\lambda_U = 0.5$ mean there's some kind of linear dependence between $X$ and $Y$?
This is what I mean…
Fred
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Generalized Pareto distribution (GPD)
I would like to understand the functional form of the Generalized Pareto distribution (GPD) presented in Wikipedia. My questions are:
what is the rationale for replacing $z$ with $\frac{x-\mu}{\sigma}$. Also, in Picture 2 in the last paragraph it…
AlexMe
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Tail dependence and copulas
I have been given this formula for upper tail dependence and read that tail dependence depends on the copula and not the marginals:
$$
\lambda_U = \lim_{a \to 1} \Pr[Y>F_Y^{-1}(a)\mid X>F_X^{-1}(a)] .
$$
Would the inverse functions $F_X^{-1}(a)$ and…
AfterWorkGuinness
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Extremal serial dependence
As part of my analysis of heavy-tailed time series of company returns, I would like to check whether extreme returns exhibit serial dependence, i.e. if extreme events are followed by extreme events.
For now, I am only interested in testing…
Olorun
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Connection between copula tail dependence and kurtosis?
Tail dependence in the pseudo-observations of bivariate copula imply that extreme upper or lower samples move together in some way suggesting correlation between the two marginals' (variables') extreme samples.
Kurtosis on the other hand describes…
develarist
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Likelihood for dependent data above a threshold
Let $(Y_t)$ a real-valued stationary Markov chain and $u$ some positive threshold. We assume that for $y>u$,
$$Y_{t+1}|\{Y_t=y\}\sim\mathcal{N}(\alpha y+\mu y^\beta,\sigma^2 y^{2\beta})$$
I want to find the maximum likelihood estimator of…
Augustin
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Tail dependence of mixture copulas
I am currently using (multivariate) mixture copulas to model a financial data set.
The mixture has two components as follows:
$$C_{mixture}=wC_1+(1-w)C_2$$
where $C_1$ and $C_2$ are copulas. I have closed form solutions for the tail dependence…
InfiniteVariance
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Meaning of parameters 'a' and 'b' within a multivariate extreme value model
It may seems a very silly question for you but it is still quite unclear to me:
What's the meaning of the parameters 'a' and 'b' presented in the Heffernan & Tawn 2004 multivariate model…
1000111000
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