simMGarch-class function

An S4 class for a nonstationary CCC model.

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 $p=q=1$. class

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.

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,])

References

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