dcc.sim {ccgarch} | R Documentation |
This function simulates data either from the original DCC-GARCH by Engle (2002) or from the Extended DCC-GARCH that has non-zero off-diagonal entries in the parameter matrices in the GARCH equation, with multivariate normal or student's t distributions.
The dimension (N) is determined by the number of elements in the a vector.
dcc.sim(nobs, a, A, B, R, dcc.para, d.f=Inf, cut=1000, model)
nobs |
a number of observations to be simulated (T) |
a |
a vector of constants in the GARCH equation (N times 1) |
A |
an ARCH parameter matrix in the GARCH equation (N times N) |
B |
a GARCH parameter matrix in the GARCH equation (N times N) |
R |
an unconditional correlation matrix (N times N) |
dcc.para |
a vector of the DCC parameters (2 times 1) |
d.f |
the degrees of freedom parameter for the t-distribution |
cut |
the number of observations to be thrown away for removing initial effects of simulation |
model |
a character string describing the model. "diagonal" for the diagonal model and "extended" for the extended (full ARCH and GARCH parameter matrices) model |
A list with components:
z |
a matrix of random draws from N(mathbf{0}, mathbf{I}). (T times N) |
std.z |
a matrix of standardised residuals. mathnormal{std.z}_{t} sim N(0, mathbf{R}_{t}) where mathbf{R}_{t} is the DCC matrix at t. If d.f is set to a finite positive real number mathbf{z}_{t} sim t_{d.f}(0, mathbf{R}_{t}) (T times N) |
dcc |
a matrix of dynamic conditional correlations (T times N^2) |
h |
a matrix of simulated volatilities (T times N) |
eps |
a matrix of time series with DCC-GARCH process (T times N) |
When "d.f=Inf", the innovations (the standardised residuals) follow the standard normal distribution. Otherwise, they follow a student's t-distribution with "d.f" degrees of freedom.
When model="diagonal", only the diagonal entries in A and B are used. If the ARCH and GARCH matrices do not satisfy the stationarity condition, the simulation is terminated.
Engle, R.F. and K. Sheppard (2001), “Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH.” Stern Finance Working Paper Series {FIN}-01-027 (Revised in Dec. 2001), New York University Stern School of Business.
Engle, R.F. (2002), “Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models.” Journal of Business and Economic Statistics 20, 339-350.
# Simulating data from the original DCC-GARCH(1,1) process nobs <- 1000; cut <- 1000; nu <- 8 a <- c(0.003, 0.005, 0.001) A <- diag(c(0.2,0.3,0.15)) B <- diag(c(0.75, 0.6, 0.8)) uncR <- matrix(c(1.0, 0.4, 0.3, 0.4, 1.0, 0.12, 0.3, 0.12, 1.0),3,3) dcc.para <- c(0.01,0.98) # for normally distributed innovations dcc.data <- dcc.sim(nobs, a, A, B, uncR, dcc.para, model="diagonal") # for t distributed innovations dcc.data.t <- dcc.sim(nobs, a, A, B, uncR, dcc.para, d.f=nu, model="diagonal")