Become an expert in R — Interactive courses, Cheat Sheets, certificates and more!
Get Started for Free

Psi

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 ‘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.

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 Σ_u are not null, the impulses measured by the Φ_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 \bold{ε}_t = P^{-1}\bold{u}_t. The moving average representation is then in the form of:

\bold{y}_t = Ψ_0 \bold{ε}_t + Ψ_1 \bold{ε}_{t-1} + Ψ \bold{ε}_{t-2} + … ,

whith Ψ_0 = P and the matrices Ψ_s are computed as Ψ_s = Φ_s P for s = 1, 2, 3, ….

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., Ψ_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)

vars

VAR Modelling

v1.5-3
GPL (>= 2)
Authors
Bernhard Pfaff [aut, cre], Matthieu Stigler [ctb]
Initial release
2018-08-05

We don't support your browser anymore

Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.