# VARff: VGLTSM family function for the Order-p Vector... In VGAMextra: Additions and Extensions of the 'VGAM' Package

 VARff R Documentation

## VGLTSM family function for the Order–p Vector Auto(R)egressive Model

### Description

Estimates an Order(p) Vector Autoregressive Models (VAR(p)) with white noise random errors by maximum likelihood estimation using Fisher scoring.

### Usage

            VARff(VAR.order = 1,
zero = c("var", "cov"),



### Arguments

 VAR.order Length–1 (positive) integer vector. The order of the VAR to be fitted. zero Integer or character - string vector. Same as MVNcov. Details at zero. lmean, lvar, lcov Same as MVNcov.

### Details

Let \boldsymbol{x}_t = (x_{1, t}, \ldots, x_{K, t})^T be a time dependent vector of responses, with index t = 1, \ldots, T, and \boldsymbol{\varepsilon}_t = (\varepsilon_{1, t}, \ldots, \varepsilon_{K, t}) white noise with covariance matrix \boldsymbol{\textrm{V}}.

VARff fits a linear model to the means of a K–variate normal distribution, where each variable, x_{i, t}, i = 1, \ldots, K, is a linear function of p–past lags of itself and past p–lags of the other variables. The model has the form

\boldsymbol{x}_t = \boldsymbol{\Phi_1} \boldsymbol{x}_{t - 1} + \cdots + \boldsymbol{\Phi_p} \boldsymbol{x}_{t - p} + \boldsymbol{\varepsilon}_t,

where \boldsymbol{\Phi_j} are K \times K matrices of coefficients, j = 1, \ldots, K, to be estimated.

The elements of the covariance matrix are intercept–only by default.

### Value

An object of class "vglmff" (see vglmff-class) to be used by VGLM/VGAM modelling functions, e.g., vglm or vgam.

### Author(s)

Victor Miranda.

MVNcov, zero, Links, ECM.EngleGran, vglm.

### Examples

set.seed(20170227)
nn <- 60
var.data <- data.frame(x2 = runif(nn, -2.5, 2.5))
var.data <- transform(var.data, y1 = rnorm(nn, 1.5 - 2 * x2, sqrt(exp(1.5))),
y2 = rnorm(nn, 1.0 - 1 * x2, sqrt(exp(0.75))),
y3 = rnorm(nn, 0.5 + 1 * x2, sqrt(exp(1.0))))

fit.var <- vglm(cbind(y1, y2, y3) ~ x2, VARff(VAR.order = 2),
trace = TRUE, data = var.data)
coef(fit.var, matrix = TRUE)

summary(fit.var)
vcov(fit.var)


VGAMextra documentation built on Nov. 2, 2023, 5:59 p.m.