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

View source: R/SOI_avg_exact.r

Calculates the Average, Minimal, and Maximal Spillover Index exactly.

1 | ```
soi_avg_exact(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 |

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

provides an algorithm to estimate average, minimum, and maximum of the spillover index over all permutations,
`soi_avg_est`

calculates these quantities exactly. Notice, however, that for large dimensions *N*, this might be quite
time- as well as memory-consuming.
If only the exact average of the spillover index is wanted, `soi_from_sot(sot_avg_exact(Sigma,A,ncores)$Average)`

should be used.

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

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 exact 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

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 the exact average, minimal,
# and maximal spillover index and determine the corresponding ordering
# of the model variables
soi_avg_exact(Sigma, A)
``` |

```
$Average
[1] 90.28282
$Min
[1] 85.71269
$Max
[1] 94.6165
$permMin
[1] 10 1 7 9 8 5 3 2 6 4
$permMax
[1] 3 2 5 1 9 6 8 10 4 7
```

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