mtCopula function

Multivariate t-Copula Volatility Model

Fits a t-copula to a k-dimensional standardized return series. The correlation matrices are parameterized by angles and the angles evolve over time via a DCC-type equation.

mtCopula(rt, g1, g2, grp = NULL, th0 = NULL, m = 0, 
                                 include.th0 = TRUE, ub=c(0.95,0.049999))

Arguments

• rt: A T-by-k data matrix of k standardized time series (after univariate volatility modeling)
• g1: lamda1 parameter, nonnegative and less than 1
• g2: lambda2 parameter, nonnegative and satisfying lambda1+lambda2 < 1.
• grp: a vector to indicate the number of assets divided into groups. Default means each individual asset forms a group.
• th0: initial estimate of theta0
• m: number of lags used to estimate the local theta-angles
• include.th0: A logical switch to include theta0 in estimation. Default is to include.
• ub: Upper bound of parameters

Returns

• estimates: Parameter estimates

• Hessian: Hessian matrix

• rho.t: Cross-correlation matrices

• theta.t: Time-varying angel matrices

References

Tsay (2014, Chapter 7). Multivariate Time Series Analysis with R and Financial Applications. John Wiley. Hoboken, NJ.

Author(s)

Ruey S. Tsay