Psi {vars} | R Documentation |
Returns the estimated orthogonalised coefficient matrices of the moving average representation of a stable VAR(p) as an array.
## S3 method for class 'varest': Psi(x, nstep=10, ...) ## S3 method for class 'vec2var': Psi(x, nstep=10, ...)
x |
An object of class ‘varest ’, generated by
VAR() , or an object of class ‘vec2var ’,
generated by vec2var() . |
nstep |
An integer specifying the number of othogonalised moving error coefficient matrices to be calculated. |
... |
Dots currently not used. |
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 Σ_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 Σ_u = PP' and the orthogonalised shocks ε_t = P^{-1}u_t. The moving average representation is then in the form of:
y_t = Psi_0 ε_t + Psi_1 ε_{t-1} + Psi ε_{t-2} + ... ,
whith Psi_0 = P and the matrices Psi_s are computed as Psi_s = Phi_s P for s = 1, 2, 3, ....
An array with dimension (K times K times nstep + 1) holding the estimated orthogonalised coefficients of the moving average representation.
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 y_t.
Bernhard Pfaff
Hamilton, J. (1994), Time Series Analysis, Princeton University Press, Princeton.
Lütkepohl, H. (2006), New Introduction to Multiple Time Series Analysis, Springer, New York.
data(Canada) var.2c <- VAR(Canada, p = 2, type = "const") Psi(var.2c, nstep=4)