Models with Margins

In tscopula: Time Series Copula Models

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

1. Gaussian ARMA Process

Construction

We generate a Gaussian ARMA model.

set.seed(13)
data1 <- 0.5 + 2*arima.sim(list(ar =0.95, ma =-0.85), 1000)
ts.plot(data1)

Estimation

A model spec can be fitted to data with the generic command fit.

copspec <- armacopula(pars = list(ar =0.01, ma =0.01))
margspec <- margin("norm")
fullspec <- tscm(copspec, margspec)
modfit <- fit(fullspec, data1, method = "full")
modfit

Plotting

As well as the copula plots we can also plot the marginal fit.

plot(modfit, plottype = "residual")
plot(modfit, plottype = "kendall")
plot(modfit, plottype = "margin")

2. VT-D-Vine Process (type 2) with Skewed Laplace Margin

Construction

copmod <- dvinecopula2(family = "joe",
                       kpacf = "kpacf_arma",
                       pars = list(ar = 0.9, ma = -0.8),
                       maxlag = 20)
vcopmod <- vtscopula(copmod,
                     Vtransform = V2p(delta = 0.5, kappa = 2))
margmod <- margin("slaplace",
                  pars = c(mu = 1, scale = 2, gamma = 0.7))
tscmmod <- tscm(vcopmod, margmod)
tscmmod

Simulation

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

Estimation

First fit a marginal model only.

margfit <- fit(margmod, data2)

Now fit the time series copula model stepwise.

tscmfit_step <- fit(tscmmod, data2)
tscmfit_step
coef(tscmfit_step)
coef(tscmmod)

Final optimization over all parameters.

tscmfit_full <- fit(tscmfit_step, data2, method = "full")
tscmfit_full

Comparison of model.

AIC(margfit, tscmfit_step, tscmfit_full)

Plotting

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

The first plots relate to the fitted copula.

plot(tscmfit_full)
plot(tscmfit_full, plottype = "kendall")

The next plot is the QQplot of the marginal fit.

plot(tscmfit_full, plottype = "margin")

The next two plots are the estimated v-transform and the estimated volatility profile function.

plot(tscmfit_full, plottype = "vtransform")
plot(tscmfit_full, plottype = "volprofile")

The final plot shows aspect of the fit of the v-transform to the data.

plot(tscmfit_full, plottype = "volproxy")

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