simMGarch-class {segMGarch}

An S4 class for a nonstationary CCC model.

Description

A specification class to create an object of a simulated piecewise constant conditional correlation (CCC) model denoted by r_t = (r_{1, t}, \ldots, r_{n, t})^T, t=1, \ldots, n with r_{i, t}= \sqrt{h_{i, t}}\epsilon_{i, t} where h_{i, t}= \omega_i(t) + \sum_{j=1}^p \alpha_{i, j}(t)r_{i, t-j}^2 + \sum_{k=1}^q \beta_{i, k}(t)h_{i, t-k}. In this package, we assume a piecewise constant CCC with p=q=1.

Slots

y

The n \times d time series.

cor_errors

The n \times d matrix of the errors.

h

The n \times d matrix of the time-varying variances.

n

Size of the time series.

d

The number of variables (assets).

r

A sparsity parameter to conrol the impact of changepoint across the series.

multp

A parameter to control the covariance of errors.

changepoints

The vector with the location of the changepoints.

pw

A logical parameter to allow for changepoints in the error covariance matrix.

a0

The vector of the parameters a0 in the individual GARCH processes denoted by \omega_i(t) in the above formula.

a1

The vector of the parameters a1 in the individual GARCH processes denoted by \alpha_i(t) in the above formula.

b1

The vector of the parameters b1 in the individual GARCH processes denoted by \beta_i(t) in the above formula.

BurnIn

The size of the burn-in sample. Note that this only applies at the first simulated segment. Default is 50.

References

Cho, Haeran, and Karolos Korkas. "High-dimensional GARCH process segmentation with an application to Value-at-Risk." arXiv preprint arXiv:1706.01155 (2017).

Examples

pw.CCC.obj <- new("simMGarch")
pw.CCC.obj <- pc_cccsim(pw.CCC.obj)
par(mfrow=c(2,2))
ts.plot(pw.CCC.obj@y[1,]);ts.plot(pw.CCC.obj@y[2,])
ts.plot(pw.CCC.obj@h[1,]);ts.plot(pw.CCC.obj@h[1,])