Description Usage Arguments Details Value See Also Examples
Appropriate marginal transforms are done before the fit using standard procedures, before the dependence model is fitted to the data. Then the posterior distribution of a measure of dependence is derived. thetafit
gives posterior samples for the extremal index θ(x,m) and chifit
does the same for the coefficient of extremal dependence χ_m(x).
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17  thetafit(ts, lapl = FALSE, nlag = 1,
R = 1000, S = 500,
u.mar = 0, u.dep,
probs = seq(u.dep, 0.9999, length.out = 30),
method.mar = c("mle", "mom","pwm"), method = c("prop", "MCi"),
silent = FALSE,
fit = TRUE, prev.fit=bayesfit(), par = bayesparams(),
submodel = c("fom", "none"), levels=c(.025,.975))
chifit(ts, lapl = FALSE, nlag = 1,
R = 1000, S = 500,
u.mar = 0, u.dep,
probs = seq(u.dep, 0.9999, length.out = 30),
method.mar = c("mle", "mom","pwm"), method = c("prop", "MCi"),
silent = FALSE,
fit = TRUE, prev.fit=bayesfit(), par = bayesparams(),
submodel = c("fom", "none"), levels=c(.025,.975))

ts 
a vector, the time series for which to estimate the extremal index θ(x,m) or the coefficient of extremal dependence χ_m(x), with x a probability level and m a runlength (see details). 
lapl 
logical; 
nlag 
the runlength; an integer larger or equal to 1. 
R 
the number of samples per MCMC iteration drawn from the sampled posterior distributions; used for the estimation of the dependence measure. 
S 
the number of posterior distributions sampled to be used for the estimation of the dependence measure. 
u.mar 
probability; threshold used for marginal transformation if 
u.dep 
probability; threshold used for the extremal dependence model. 
probs 
vector of probabilities; the values of x for which to evaluate θ(x,m) or χ_m(x). 
method.mar 
a character string defining the method used to estimate the marginal GPD; either 
method 
a character string defining the method used to estimate the dependence measure; either 
silent 
logical ( 
fit 
logical; 
prev.fit 
an object of class 'bayesfit'. Needed if 
par 
an object of class ' 
submodel 
a character string, either 
levels 
vector of probabilites; the quantiles of the posterior distribution of the extremal measure to be computed. 
The subasymptotic extremal index is defined as
θ(x,m) = Pr(X_1 < x,…,X_m < x  X_0 > x),
whose limit as x and m go to ∞appropriately is the extremal index θ. The extremal index can be interpreted as the inverse of the asymptotic mean cluster size (see thetaruns)
.
The subasymptotic coefficient of extremal dependence is
χ_m(x) = Pr(X_m > x  X_0 > x),
whose limit χ defines asymptotic dependence (χ > 0) or asymptotic independence (χ = 0).
Both types of extremal dependence measures can be estimated either using a
* proportion method (method == "prop"
), sampling from the conditional probability given X_0 > x and counting the proportion of sampled points falling in the region of interest, or
* Monte Carlo integration (method == "MCi"
), sampling replicates from the marginal exponential tail distribution and evaluating the conditional tail distribution in these replicates, then taking their mean as an approximation of the integral.
submodel == "fom"
imposes a first order Markov structure to the model, namely a geometrical decrease in α and a constant β across lags, i.e. α_j = α^j and β_j = β, j=1,…,m.
An object of class 'depmeasure', containing a subset of:
bayesfit 
An object of class 'bayesfit' 
theta 
An array with dimensions 
distr 
An array with dimensions 
chi 
An array with dimensions 
probs 

levels 

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28  ## generate data from an AR(1)
## with Gaussian marginal distribution
n < 10000
dep < 0.5
ar < numeric(n)
ar[1] < rnorm(1)
for(i in 2:n)
ar[i] < rnorm(1, mean=dep*ar[i1], sd=1dep^2)
plot(ar, type="l")
plot(density(ar))
grid < seq(3,3,0.01)
lines(grid, dnorm(grid), col="blue")
## rescale the margin (focus on dependence)
ar < qlapl(pnorm(ar))
## fit the data
params < bayesparams()
params$maxit < 100 # bigger numbers would be
params$burn < 10 # more sensible...
params$thin < 4
theta < thetafit(ts=ar, R=500, S=100, u.mar=0.95, u.dep=0.98,
probs = c(0.98, 0.999), par=params)
## or, same thing in two steps to control fit output before computing theta:
fit < depfit(ts=ar, u.mar=0.95, u.dep=0.98, par=params)
plot(fit)
theta < thetafit(ts=ar, R=500, S=100, u.mar=0.95, u.dep=0.98,
probs = c(0.98, 0.999), fit=FALSE, prev.fit=fit)

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