VARMA: Vector Autoregressive Moving-Average Models
In MTS: All-Purpose Toolkit for Analyzing Multivariate Time Series (MTS) and Estimating Multivariate Volatility Models

VARMA

R Documentation

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.

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)

MTS documentation built on April 11, 2022, 5:07 p.m.