VARMACpp function

Vector Autoregressive Moving-Average Models (Cpp)

Performs conditional maximum likelihood estimation of a VARMA model. Multivariate Gaussian likelihood function is used. This is the same function as VARMA, with the likelihood function implemented in C++ for efficiency.

VARMACpp(da, p = 0, q = 0, include.mean = T, 
    fixed = NULL, beta=NULL, sebeta=NULL, 
    prelim = F, details = F, thres = 2)

Arguments

• da: Data matrix (T-by-k) of a k-dimensional time series with sample size T.
• p: AR order
• q: MA order
• include.mean: A logical switch to control estimation of the mean vector. Default is to include the mean in estimation.
• fixed: A logical matrix to control zero coefficients in estimation. It is mainly used by the command refVARMA.
• beta: Parameter estimates to be used in model simplification, if needed
• sebeta: Standard errors of parameter estimates for use in model simplification
• prelim: A logical switch to control preliminary estimation. Default is none.
• details: A logical switch to control the amount of output.
• thres: A threshold used to set zero parameter constraints based on individual t-ratio. Default is 2.

Details

The fixed command is used for model refinement

Returns

• data: Observed data matrix

• ARorder: VAR order

• MAorder: VMA order

• cnst: A logical switch to include the mean vector

• coef: Parameter estimates

• secoef: Standard errors of the estimates

• residuals: Residual matrix

• Sigma: Residual covariance matrix

• aic,bic: Information criteria of the fitted model

• Phi: VAR coefficients

• Theta: VMA coefficients

• Ph0: The constant vector

References

Tsay (2014, Chapter 3). Multivariate Time Series Analysis with R and Financial Applications. John Wiley. Hoboken, NJ.

Author(s)

Ruey S. Tsay

See Also

VARMA

Examples

phi=matrix(c(0.2,-0.6,0.3,1.1),2,2); theta=matrix(c(-0.5,0,0,-0.5),2,2)
sigma=diag(2)
m1=VARMAsim(300,arlags=c(1),malags=c(1),phi=phi,theta=theta,sigma=sigma)
zt=m1$series
m2=VARMA(zt,p=1,q=1,include.mean=FALSE)