VARMA {MTS}

Vector Autoregressive Moving-Average Models

Description

Performs conditional maximum likelihood estimation of a VARMA model. Multivariate Gaussian likelihood function is used.

Usage

VARMA(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

Value

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

Author(s)

Ruey S. Tsay

References

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

See Also

refVARMA

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)