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.

### See Also

`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")

[Package vars version 1.5-3 Index]