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

Calculates an estimate of the average, the minimum, and the maximum spillover index based on different permutations.

1 | ```
soi_avg_est(Sigma, A, ncores = 1, ...)
``` |

`Sigma` |
Either a covariance matrix or a list thereof. |

`A` |
Either a 3-dimensional array with A[,,h] being MA coefficient matrices of the same dimension as |

`ncores` |
Number of cores. Missing ncores or |

`...` |
Further arguments, especially |

The spillover index introduced by Diebold and Yilmaz (2009) (see References) depends on the ordering of the model variables.
While `soi_avg_exact`

provides a fast algorithm for exact calculation of average, minimum, and maximum of the spillover index over all permutations,
there might be reasons to prefer to estimate these quantities using a limited number of permutations (mainly to save time when
*N* is large). This is exactly what `soi_avg_est`

does.

The typical application of the 'list' version of `soi_avg_est`

is a rolling windows approach when `Sigma`

and `A`

are lists representing the corresponding quantities at different points in time
(rolling windows).

The 'single' version returns a list containing the estimated average, minimal, and maximal spillover index as well as permutations that generated the minimal and maximal value. The 'list' version returns a list consisting of three vectors (the average, minimal, and maximal spillover index values) and two matrices (the columns of which are the permutations generating the minima and maxima).

Stefan Kloessner (S.Kloessner@mx.uni-saarland.de),

with contributions by Sven Wagner (sven.wagner@mx.uni-saarland.de)

[1] Diebold, F. X. and Yilmaz, K. (2009): Measuring financial asset return and volatitliy spillovers, with application to global equity markets, Economic Journal 199(534): 158-171.

[2] Kloessner, S. and Wagner, S. (2012): Exploring All VAR Orderings for Calculating Spillovers? Yes, We Can! - A Note on Diebold and Yilmaz (2009), Journal of Applied Econometrics 29(1): 172-179

`fastSOM-package`

, `soi_avg_exact`

1 2 3 4 5 6 7 8 9 10 | ```
# generate randomly positive definite matrix Sigma of dimension N
N <- 10
Sigma <- crossprod(matrix(rnorm(N*N),nrow=N))
# generate randomly coefficient matrices
H <- 10
A <- array(rnorm(N*N*H),dim=c(N,N,H))
# calculate estimates of the average, minimal,
# and maximal spillover index and determine the corresponding ordering
# of the model variables
soi_avg_est(Sigma, A)
``` |

```
$Average
[1] 91.09991
$Min
[1] 87.78032
$Max
[1] 94.19889
$permMin
[1] 7 5 9 2 4 10 1 8 6 3
$permMax
[1] 1 10 3 9 6 4 5 7 2 8
```

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