# VMACpp: Vector Moving Averge Model (Cpp) In MTS: All-Purpose Toolkit for Analyzing Multivariate Time Series (MTS) and Estimating Multivariate Volatility Models

## Description

Performs VMA estimation using the conditional multivariate Gaussian likelihood function. This is the same function as VMA, with the likelihood function implemented in C++ for efficiency.

## Usage

 ```1 2 3``` ```VMACpp(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 parameeter to zero. Deault is 2.

## Value

 `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

Ruey S. Tsay

## References

Tsay (2014, Chapter 3).

 ```1 2 3 4``` ```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=VMACpp(zt,q=1,include.mean=FALSE) ```