depfit: Dependence model fit

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"))

Value

An object of class 'bayesfit' with elements:

a: posterior trace of \(\alpha\).
b: posterior trace of \(\beta\).
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 \(\alpha\) and \(\beta\).
len: length of the returned traces.

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 \(\alpha_j\) and \(\beta_j\) (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 \(\alpha=\beta=0\) (see examples).

Examples

Run this code

## 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")