Phi {vars} | R Documentation |
Returns the estimated coefficient matrices of the moving average representation of a stable VAR(p), of an SVAR as an array or a converted VECM to VAR.
## S3 method for class 'varest': Phi(x, nstep=10, ...) ## S3 method for class 'svarest': Phi(x, nstep=10, ...) ## S3 method for class 'svecest': Phi(x, nstep=10, ...) ## S3 method for class 'vec2var': Phi(x, nstep=10, ...)
x |
An object of class ‘varest ’, generated by
VAR() , or an object of class ‘svarest ’,
generated by SVAR() , or an object of class
‘svecest ’, generated by SVEC() , or an object
of class ‘vec2var ’, generated by vec2var() . |
nstep |
An integer specifying the number of moving error coefficient matrices to be calculated. |
... |
Currently not used. |
If the process y_t is stationary (i.e. I(0), it has a Wold moving average representation in the form of:
y_t = Phi_0 u_t + Phi_1 u_{t-1} + Phi u_{t-2} + ... ,
whith Phi_0 = I_k and the matrices Phi_s can be computed recursively according to:
Phi_s = sum_{j=1}^s Phi_{s-j} A_j quad s = 1, 2, ... ,
whereby A_j are set to zero for j > p. The matrix elements
represent the impulse responses of the components of y_t
with respect to the shocks u_t. More precisely, the
(i, j)th element of the matrix Phi_s mirrors the expected
response of y_{i, t+s} to a unit change of the variable
y_{jt}.
In case of a SVAR, the impulse response matrices are given by:
Theta_i = Phi_i A^{-1} B quad .
Albeit the fact, that the Wold decomposition does not exist for nonstationary processes, it is however still possible to compute the Phi_i matrices likewise with integrated variables or for the level version of a VECM. However, a convergence to zero of Phi_i as i tends to infinity is not ensured; hence some shocks may have a permanent effect.
An array with dimension (K times K times nstep + 1) holding the estimated coefficients of the moving average representation.
The first returned array element is the starting value, i.e., Phi_0.
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") Phi(var.2c, nstep=4)