R: Estimation of a VAR(p)

VAR {vars}

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} + … + 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, …, 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()`.

Author(s)

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.

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")

[Package vars version 1.5-0 Index]