VMA function

Vector Moving Average Model

Performs VMA estimation using the conditional multivariate Gaussian likelihood function

VMA(da, q = 1, include.mean = T, fixed = NULL, 
    beta=NULL, sebeta=NULL, prelim = F, 
    details = F, thres = 2)

Arguments

• da: Data matrix of a k-dimensional VMA process with each column containing one time series
• q: The order of VMA model
• include.mean: A logical switch to include the mean vector. The default is to include the mean vector in estimation.
• fixed: A logical matrix used to fix parameter to zero
• beta: Parameter estimates for use in model simplification
• sebeta: Standard errors of parameter estimates for use in model simplification
• prelim: A logical switch to select parameters to be included in estimation
• details: A logical switch to control the amount of output
• thres: Threshold for t-ratio used to fix parameter to zero. Default is 2.

Returns

• data: The data of the observed time series

• MAorder: The VMA order

• cnst: A logical switch to include the mean vector

• coef: Parameter estimates

• secoef: Standard errors of the parameter estimates

• residuals: Residual series

• Sigma: Residual covariance matrix

• Theta: The VAR coefficient matrix

• mu: The constant vector

• aic,bic: The information criteria of the fitted model

References

Tsay (2014, Chapter 3).

Author(s)

Ruey S. Tsay

Examples

theta=matrix(c(0.5,0.4,0,0.6),2,2); sigma=diag(2)
m1=VARMAsim(200,malags=c(1),theta=theta,sigma=sigma)
zt=m1$series
m2=VMA(zt,q=1,include.mean=FALSE)