# VAR: Estimation of a VAR(p) In vars: VAR Modelling

 VAR R Documentation

## 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"))
## S3 method for class 'varest'
print(x, digits = max(3, getOption("digits") - 3), ...)


### 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. x Object with class attribute ‘varest’. digits the number of significant digits to use when printing. ... further arguments passed to or from other methods.

### 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.

### 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().

Bernhard Pfaff

### References

Hamilton, J. (1994), Time Series Analysis, Princeton University Press, Princeton.

Lütkepohl, H. (2006), New Introduction to Multiple Time Series Analysis, Springer, New York.

summary, plot, coef, residuals, fitted, predict, irf, fevd, Phi, Psi, normality.test, arch.test, serial.test, 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")


vars documentation built on June 24, 2024, 9:08 a.m.