soi {fastSOM}

Calculation of the Spillover Index

Description

This function calculates the spillover index as proposed by Diebold and Yilmaz (2009, see References).

Usage

soi(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 if Sigma is a list of matrices. 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.

...

Further arguments, especially perm which is used to reorder variables. If perm is missing, then the original ordering of the model variables will be used. If perm is a permutation of 1:N, then the spillover index for the model with variables reordered according to perm will be calculated.

Details

The spillover index was introduced by Diebold and Yilmaz in 2009 (see References). It is based on a variance decompostion of the forecast error variances of an N-dimensional MA(\infty) process. The underlying idea is to decompose the forecast error of each variable into own variance shares and cross variance shares. The latter are interpreted as contributions of shocks of one variable to the error variance in forecasting another variable (see also sot). The spillover index then is a number between 0 and 100, describing the relative amount of forecast error variances that can be explained by shocks coming from other variables in the model.

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

Value

Returns a single numeric value or a list thereof.

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

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 spillover index
soi(Sigma, A)