dep2fit: Dependence model fit (stepwise)
In tsxtreme: Bayesian Modelling of Extremal Dependence in Time Series

Description Usage Arguments Details Value See Also Examples

View source: R/ht2fit.R

The conditional Heffernan–Tawn model is used to fit the dependence in time of a stationary series. A standard 2-stage procedure is used.

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dep2fit(ts, u.mar = 0, u.dep,
        lapl = FALSE, method.mar = c("mle","mom","pwm"),
        nlag = 1, conditions = TRUE)

`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 of `"mom"` for method of moments. Defaults to `"mle"`.
`nlag`	integer; number of lags to be considered when modelling the dependence in time.
`conditions`	logical; should conditions on α and β be set? (see Details) Defaults to `TRUE`.

Consider a stationary time series (X_t) with Laplace marginal distribution; the fitting procedure consists of fitting

X_t = α_t * x_0 + x_0^{β_t} * Z_t, t=1,…,m,

with m the number of lags considered. A likelihood is maximised assuming Z_t ~ N(μ_t, σ^2_t), then an empirical distribution for the Z_t is derived using the estimates of α_t and β_t and the relation

Z_t = (X_t - α_t * x_0) / x_0^{β_t}.

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 (α,β) live.

`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 `alpha` and `beta` given by the hessian matrix of the likelihood function used in the first step of the inference procedure.

depfit, theta2fit

## 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