Description Usage Arguments Details Value Author(s) References See Also Examples

Estimates an SVEC by utilising a scoring algorithm.

1 2 3 4 |

`x` |
Object of class ‘ |

`LR` |
Matrix of the restricted long run impact matrix. |

`SR` |
Matrix of the restricted contemporaneous impact matrix. |

`r` |
Integer, the cointegration rank of x. |

`start` |
Vector of starting values for |

`max.iter` |
Integer, maximum number of iteration. |

`conv.crit` |
Real, convergence value of algorithm.. |

`maxls` |
Real, maximum movement of the parameters between two iterations of the scoring algorithm. |

`lrtest` |
Logical, over-identification LR test, the result is set
to |

`boot` |
Logical, if |

`runs` |
Integer, number of bootstrap replications. |

`digits` |
the number of significant digits to use when printing. |

`...` |
further arguments passed to or from other methods. |

Consider the following reduced form of a k-dimensional vector error correction model:

*
A Δ \bold{y}_t = Π \bold{y}_{t-1} + Γ_1 Δ
\bold{y}_{t-1} + … + Γ_p Δ \bold{y}_{t-p + 1} +
\bold{u}_t \quad .*

This VECM has the following MA representation:

*
\bold{y}_t = Ξ ∑_{i=1}^t \bold{u}_i + Ξ^*(L)\bold{u}_t +
\bold{y}_0^* \quad ,*

with *Ξ = β_{\perp} (α_{\perp}'(I_K -
∑_{i=1}^{p-1}Γ_i)β_{\perp} )^{-1}α_{\perp}'* and
*Ξ^*(L)* signifies an infinite-order polynomial in the lag
operator with coefficient matrices *Ξ^*_j* that tends to zero
with increasing size of *j*.

Contemporaneous restrictions on the impact matrix *B* must be
supplied as zero entries in `SR`

and free parameters as `NA`

entries. Restrictions on the long run impact matrix *Ξ B* have
to be supplied likewise. The unknown parameters are estimated by
maximising the concentrated log-likelihood subject to the imposed
restrictions by utilising a scoring algorithm on:

*
\ln L_c(A, B) = - \frac{KT}{2}\ln(2π) + \frac{T}{2}\ln|A|^2 -
\frac{T}{2}\ln|B|^2 - \frac{T}{2}tr(A'B'^{-1}B^{-1}A\tilde{Σ}_u)
*

with *\tilde{Σ}_u* signifies the reduced form
variance-covariance matrix and *A* is set equal to the identity
matrix *I_K*.

If ‘`start`

’ is not set, then normal random numbers are used as
starting values for the unknown coefficients. In case of an
overidentified SVEC, a likelihood ratio statistic is computed according to:

*
LR = T(\ln\det(\tilde{Σ}_u^r) - \ln\det(\tilde{Σ}_u))
\quad , *

with *\tilde{Σ}_u^r* being the restricted variance-covariance
matrix and *\tilde{Σ}_u* being the variance covariance matrix
of the reduced form residuals. The test statistic is distributed as
*χ^2(K*(K+1)/2 - nr)*, where *nr* is equal to the number of
restrictions.

A list of class ‘`svecest`

’ with the following elements is
returned:

`SR` |
The estimated contemporaneous impact matrix. |

`SRse` |
The standard errors of the contemporaneous impact matrix,
if |

`LR` |
The estimated long run impact matrix. |

`LRse` |
The standard errors of the long run impact matrix,
if |

`Sigma.U` |
The variance-covariance matrix of the reduced form
residuals times 100, |

`Restrictions` |
Vector, containing the ranks of the restricted long run and contemporaneous impact matrices. |

`LRover` |
Object of class ‘ |

`start` |
Vector of used starting values. |

`type` |
Character, type of the SVEC-model. |

`var` |
The ‘ |

`LRorig` |
The supplied long run impact matrix. |

`SRorig` |
The supplied contemporaneous impact matrix. |

`r` |
Integer, the supplied cointegration rank. |

`iter` |
Integer, the count of iterations. |

`call` |
The |

Bernhard Pfaff

Amisano, G. and C. Giannini (1997), *Topics in Structural VAR
Econometrics*, 2nd edition, Springer, Berlin.

Breitung, J., R. BrÃ¼ggemann and H. LÃ¼tkepohl (2004), Structural vector
autoregressive modeling and impulse responses, in H. LÃ¼tkepohl and
M. KrÃ¤tzig (editors), *Applied Time Series Econometrics*,
Cambridge University Press, Cambridge.

Hamilton, J. (1994), *Time Series Analysis*, Princeton
University Press, Princeton.

LÃ¼tkepohl, H. (2006), *New Introduction to Multiple Time Series
Analysis*, Springer, New York.

1 2 3 4 5 6 7 8 9 10 11 | ```
data(Canada)
vecm <- ca.jo(Canada[, c("prod", "e", "U", "rw")], type = "trace",
ecdet = "trend", K = 3, spec = "transitory")
SR <- matrix(NA, nrow = 4, ncol = 4)
SR[4, 2] <- 0
SR
LR <- matrix(NA, nrow = 4, ncol = 4)
LR[1, 2:4] <- 0
LR[2:4, 4] <- 0
LR
SVEC(vecm, LR = LR, SR = SR, r = 1, lrtest = FALSE, boot = FALSE)
``` |

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