Copula Processes with V-Transforms

In tscopula: Time Series Copula Models

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
library(tscopula)

All types of copula process can be combined with a v-transform to model volatile time series.

1. VT-ARMA Copula Processes

VT-ARMA processes are created by adding a v-transform to an armacopula process using the command vtscopula. The generic commands sim, fit and plot also work for these processes.

VT-ARMA(1,1) Example

This example uses a ARMA(1,1) copula and an off-centre linear v-transform. We set up the model and generate some data.

vtarma11 <- vtscopula(armacopula(list(ar = 0.95, ma = -0.85)),
  Vtransform = Vlinear(delta = 0.6))
vtarma11
set.seed(19)
data <- sim(vtarma11, 2000)
ts.plot(data)

We now fit the model with a fixed value for the fulcrum parameter $\delta$ and plot the results. (More on fulcrum choice next.)

vtarma11spec <- vtscopula(armacopula(list(ar = 0, ma = 0)), Vtransform = Vlinear(delta = 0.6))
vtarma11fit <- fit(vtarma11spec, data)
vtarma11fit

plot(vtarma11fit)
plot(vtarma11fit, plottype = "vtransform")
plot(vtarma11fit, plottype = "kendall" )

Optimization over the fulcrum parameter $\delta$ does not take place. To identify a reasonable value for $\delta$ we can carry a profile likelihood analysis using different fixed values for the fulcrum parameter.

profilefulcrum(data, tscopula = vtarma11spec, locations = seq(from = 0, to = 1, length = 11))
abline(v = 0.6)

2. VT-D-Vine Copula Processes (type 2)

VT-D-Vine processes are created by adding a v-transform to an dvinecopula2 object using the command vtscopula. The generic commands sim, fit and plot also work for these processes.

Construction

We add a 2-parameter V-transform.

copmod <- dvinecopula2(family = "joe",
                       kpacf = "kpacf_arma",
                       pars = list(ar = 0.9, ma = -0.85),
                       maxlag = 20)
vcopmod <- vtscopula(copmod,
  Vtransform = V2p(delta = 0.6, kappa = 0.8)
)
vcopmod

Simulation

set.seed(13)
data2 <- sim(vcopmod, n = 2000)
hist(data2)
ts.plot(data2)

Estimation

copspec_Joe <- dvinecopula2(family = "joe",
                            pars = list(ar = 0, ma = 0),
                            maxlag = 30)
vcopspec <- vtscopula(copspec_Joe, V2p(delta = 0.6))
vcopfit <- fit(vcopspec, data2, 
               tsoptions = list(hessian = TRUE),
               control = list(maxit = 1000))
vcopfit
coef(vcopfit)
coef(vcopmod)

Plotting

We can plot the estimated v-transform and well as the goodness-of-fit plots for the dvinecopula2 object based on Kendall rank correlations.

plot(vcopfit, plottype = "vtransform")
plot(vcopfit, plottype = "kendall")
plot(vcopfit, plottype = "residual")

tscopula documentation built on May 29, 2024, 5:53 a.m.