sot_avg_exact {fastSOM}

Calculation of the Exact Values for Average, Minimal, and Maximal Entries of a Spillover Table

Description

Calculates the exact values of the average, the minimum, and the maximum entries of a spillover tables based on different permutations.

Usage

sot_avg_exact(Sigma, A, ncores = 1)

Arguments

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 Sigma or a list thereof.

ncores

Number of cores, only relevant for 'list' version. In this case, missing ncores or ncores=1 means no parallelization (just one core is used), ncores=0 means automatic detection of the number of available cores, any other integer determines the maximal number of cores to be used.

Details

The spillover tables introduced by Diebold and Yilmaz (2009) (see References) depend on the ordering of the model variables. While sot_avg_est provides an algorithm to estimate average, minimal, and maximal values of the spillover table over all permutations, sot_avg_est calculates these quantities exactly. Notice, however, that for large dimensions N, this might be quite time- as well as memory-consuming.

The typical application of the 'list' version of sot_avg_exact is a rolling windows approach when Sigma and A are lists representing the corresponding quantities at different points in time (rolling windows).

Value

The 'single' version returns a list containing the exact average, minimal, and maximal values for the spillover table. The 'list' version returns a list with three elements (Average, Minimum, Maximum) which themselves are lists of the corresponding tables.

Author(s)

Stefan Kloessner ([e-mail]),
with contributions by Sven Wagner ([e-mail])

References

[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

See Also

fastSOM-package, sot_avg_est

Examples

# 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 entries within a spillover table
sot_avg_exact(Sigma, A)