VARff: VGLTSM family function for the Order-p Vector...

View source: R/VARff.R

VARffR Documentation

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


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


            VARff(VAR.order = 1,
                  zero = c("var", "cov"),
                  lmean = "identitylink",
                  lvar  = "loglink",
                  lcov  = "identitylink")



Length–1 (positive) integer vector. The order of the VAR to be fitted.


Integer or character - string vector. Same as MVNcov. Details at zero.

lmean, lvar, lcov

Same as MVNcov.


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.


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


Victor Miranda.

See Also

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


nn <- 60 <- data.frame(x2 = runif(nn, -2.5, 2.5)) <- transform(, 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 =
coef(fit.var, matrix = TRUE)


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