vars (version 1.1-9)

VAR: Estimation of a VAR(p)

Description

Estimation of a VAR by utilising OLS per equation.

Usage

VAR(y, p = 1, type = c("const", "trend", "both", "none"),
season = NULL, exogen = NULL, lag.max = NULL,
ic = c("AIC", "HQ", "SC", "FPE"))

Arguments

y

Data item containing the endogenous variables

p

Integer for the lag order (default is p=1).

type

Type of deterministic regressors to include.

season

Inlusion of centered seasonal dummy variables (integer value of frequency).

exogen

Inlusion of exogenous variables.

lag.max

Integer, determines the highest lag order for lag length selection according to the choosen ic.

ic

Character, selects the information criteria, if lag.max is not NULL.

Value

• A list with class attribute varest holding the following elements:
• varresult
  list of lm objects.
• datamat
  The data matrix of the endogenous and explanatory variables.
• y
  The data matrix of the endogenous variables
• type
  A character, specifying the deterministic regressors.
• p
  An integer specifying the lag order.
• K
  An integer specifying the dimension of the VAR.
• obs
  An integer specifying the number of used observations.
• totobs
  An integer specifying the total number of observations.
• restrictions
  Either NULL or a matrix object containing the zero restrictions of the VAR(p).
• call
  The call to VAR().

encoding

latin1

concept

• VAR
• Vector autoregressive model
• VAR

Details

Estimates a VAR by OLS per equation. The model is of the following form: $$\bold{y}_t = A_1 \bold{y}_{t-1} + \ldots + A_p \bold{y}_{t-p} + CD_t + \bold{u}_t$$ where $\bold{y}_t$ is a $K \times 1$ vector of endogenous variables and $u_t$ assigns a spherical disturbance term of the same dimension. The coefficient matrices $A_1, \ldots, A_p$ are of dimension $K \times K$. In addition, either a constant and/or a trend can be included as deterministic regressors as well as centered seasonal dummy variables and/or exogenous variables (term $CD_T$, by setting the type argument to the corresponding value and/or setting season to the desired frequency (integer) and/or providing a matrix object for exogen, respectively. The default for type is const and for season and exogen the default is set to NULL. If for lag.max an integer value is provided instead of NULL (the default), the lag length is determined by the selected information criteria in ic, the default is Akaike.

References

Hamilton, J. (1994), Time Series Analysis, Princeton University Press, Princeton. L�tkepohl, H. (2006), New Introduction to Multiple Time Series Analysis, Springer, New York.

See Also

summary, plot, coef, residuals, fitted, predict, irf, fevd, Phi, Psi, normality, arch, serial, VARselect, logLik

Examples

data(Canada)
VAR(Canada, p = 2, type = "none")
VAR(Canada, p = 2, type = "const")
VAR(Canada, p = 2, type = "trend")
VAR(Canada, p = 2, type = "both")