| Psi {vars} | R Documentation |
Coefficient matrices of the orthogonalised MA represention
Description
Returns the estimated orthogonalised coefficient matrices of the moving average representation of a stable VAR(p) as an array.
Usage
## S3 method for class 'varest'
Psi(x, nstep=10, ...)
## S3 method for class 'vec2var'
Psi(x, nstep=10, ...)
Arguments
x |
An object of class ‘ |
nstep |
An integer specifying the number of othogonalised moving error coefficient matrices to be calculated. |
... |
Dots currently not used. |
Details
In case that the components of the error process are instantaneously
correlated with each other, that is: the off-diagonal elements of the
variance-covariance matrix \Sigma_u are not null, the impulses
measured by the \Phi_s matrices, would also reflect disturbances
from the other variables. Therefore, in practice a Choleski
decomposition has been propagated by considering \Sigma_u = PP' and the
orthogonalised shocks \bold{\epsilon}_t = P^{-1}\bold{u}_t. The
moving average representation is then in the form of:
\bold{y}_t = \Psi_0 \bold{\epsilon}_t + \Psi_1
\bold{\epsilon}_{t-1} + \Psi \bold{\epsilon}_{t-2} + \ldots ,
whith \Psi_0 = P and the matrices \Psi_s are computed
as \Psi_s = \Phi_s P for s = 1, 2, 3, \ldots.
Value
An array with dimension (K \times K \times nstep + 1) holding the
estimated orthogonalised coefficients of the moving average representation.
Note
The first returned array element is the starting value, i.e.,
\Psi_0. Due to the utilisation of the Choleski decomposition,
the impulse are now dependent on the ordering of the vector elements
in \bold{y}_t.
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
Examples
data(Canada)
var.2c <- VAR(Canada, p = 2, type = "const")
Psi(var.2c, nstep=4)