depfit: Dependence model fit

In tsxtreme: Bayesian Modelling of Extremal Dependence in Time Series

Description

Bayesian semiparametrics are used to fit the Heffernan–Tawn model to time series. Options are available to impose a structure in time on the model.

Usage

depfit(ts, u.mar = 0, u.dep=u.mar,
    lapl = FALSE, method.mar=c("mle","mom","pwm"),  nlag = 1,
    par = bayesparams(),
    submodel = c("fom", "none", "ugm"))

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. u.dep can be lower than u.mar.
lapl	logical; is ts on the Laplace scale already? The default (FALSE) assumes unknown marginal distribution.
method.mar	a character string defining the method used to estimate the marginal GPD; either "mle" for maximum likelihood or "mom" for method of moments or "pwm" for probability weighted moments. Defaults to "mle".
nlag	integer; number of lags to be considered when modelling the dependence in time.
par	an object of class 'bayesparams'.
submodel	a character string; "fom" for first order Markov, "none" for no particular time structure, or "ugm" for univariate Gaussian mixture (see details).

Details

submodel can be "fom" to impose a first order Markov structure on the model parameters α_j and β_j (see thetafit for more details); it can take the value "none" to impose no particular structure in time; it can also be "ugm" which can be applied to density estimation, as it corresponds to setting α=β=0 (see examples).

Value

An object of class 'bayesfit' with elements:

a	posterior trace of α.
b	posterior trace of β.
sd	posterior trace of the components' standard deviations.
mean	posterior trace of the components' means.
w	posterior trace of the components' assigned weights.
prec	posterior trace of the precision parameter.
noo	posterior trace of the number of observations per component.
noc	posterior trace of the number of components containing at least one observation.
prop.sd	trace of proposal standard deviations in the 5+3 regions of the adaption scheme for α and β.
len	length of the returned traces.

See Also

thetafit, chifit

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)
  
## rescale the margin
ar <- qlapl(pnorm(ar))

## fit the data
params <- bayesparams()
params$maxit <- 100# bigger numbers would be
params$burn  <- 10 # more sensible...
params$thin  <- 4
fit <- depfit(ts=ar, u.mar=0.95, u.dep=0.98, par=params)

########
## density estimation with submodel=="ugm"
data <- MASS::galaxies/1e3
dens <- depfit(ts=data, par=params, submodel="ugm")

tsxtreme documentation built on April 24, 2021, 1:07 a.m.