# sVARMACpp: Seasonal VARMA Model Estimation (Cpp) In MTS: All-Purpose Toolkit for Analyzing Multivariate Time Series (MTS) and Estimating Multivariate Volatility Models

## Description

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

## Usage

 `1` ```sVARMACpp(da, order, sorder, s, include.mean = T, fixed = NULL, details = F, switch = F) ```

## Arguments

 `da` A T-by-k data matrix of a k-dimensional seasonal time series `order` Regular order (p,d,q) of the model `sorder` Seasonal order (P,D,Q) of the model `s` Seasonality. s=4 for quarterly data and s=12 for monthly series `include.mean` A logical switch to include the mean vector. Deafult is to include the mean `fixed` A logical matrix to set zero parameter constraints `details` A logical switch for output `switch` A logical switch to exchange the ordering of the regular and seasonal VMA factors. Default is theta(B)*Theta(B).

## Details

Estimation of a sesonal VARMA model

## Value

 `data` The data matrix of the observed k-dimensional time series `order` The reqular order (p,d,q) `sorder` The seasonal order (P,D,Q) `period` Seasonality `cnst` A logical switch for the constant term `ceof` Parameter estimates for use in model simplification `secoef` Standard errors of the parameter estimates `residuals` Residual series `Sigma` Residual covariance matrix `aic,bic` Information criteria of the fitted model `regPhi` Regular AR coefficients, if any `seaPhi` Seasonal AR coefficients `regTheta` Regular MA coefficients `seaTheta` Seasonal MA coefficients `Ph0` The constant vector, if any `switch` The logical switch to change the ordering of matrix product

Ruey S. Tsay

## References

Tsay (2014, Chapter 6). Multivariate Time Series Analysis with R and Financial Applications. John Wiley. Hoboken, NJ.