dep2fit {tsxtreme} | R Documentation |
Dependence model fit (stepwise)
Description
The conditional Heffernan–Tawn model is used to fit the dependence in time of a stationary series. A standard 2-stage procedure is used.
Usage
dep2fit(ts, u.mar = 0, u.dep,
lapl = FALSE, method.mar = c("mle","mom","pwm"),
nlag = 1, conditions = TRUE)
Arguments
ts |
numeric vector; time series to be fitted. |
u.mar |
marginal threshold; used when transforming the time series to Laplace scale. |
u.dep |
dependence threshold; level above which the dependence is modelled. |
lapl |
logical; is |
method.mar |
a character string defining the method used to estimate the marginal GPD; either |
nlag |
integer; number of lags to be considered when modelling the dependence in time. |
conditions |
logical; should conditions on |
Details
Consider a stationary time series with Laplace marginal distribution; the fitting procedure consists of fitting
with the number of lags considered. A likelihood is maximised assuming
, then an empirical distribution for the
is derived using the estimates of
and
and the relation
conditions
implements additional conditions suggested by Keef, Papastathopoulos and Tawn (2013) on the ordering of conditional quantiles. These conditions help with getting a consistent fit by shrinking the domain in which live.
Value
alpha |
parameter controlling the conditional extremal expectation. |
beta |
parameter controlling the conditional extremal expectation and variance. |
res |
empirical residual of the model. |
pars.se |
vector of length 2 giving the estimated standard errors for |
See Also
Examples
## 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[i-1], sd=1-dep^2)
plot(ar, type="l")
plot(density(ar))
grid <- seq(-3,3,0.01)
lines(grid, dnorm(grid), col="blue")
## rescale margin
ar <- qlapl(pnorm(ar))
## fit model without constraints...
fit1 <- dep2fit(ts=ar, u.mar = 0.95, u.dep=0.98, conditions=FALSE)
fit1$a; fit1$b
## ...and compare with a fit with constraints
fit2 <- dep2fit(ts=ar, u.mar = 0.95, u.dep=0.98, conditions=TRUE)
fit2$a; fit2$b# should be similar, as true parameters lie well within the constraints