ctmcd (version 1.4.4)

gmDA: Diagonal Adjustment

Description

Function for deriving a Markov generator matrix estimate based on the diagonal adjustment method of Israel et al., 2001

Usage

gmDA(tmrel, te, logmethod = "Eigen")

Value

generator matrix estimate

Arguments

tmrel

matrix of relative transition frequencies

te

time elapsed in transition process

logmethod

method for computation of matrix logarithm, by default eigendecomposition is chosen (see ?logm from expm package for more information)

Author

Marius Pfeuffer

Details

A candidate solution is derived by the matrix logarithm and then adjusted in order to fulfil the properties of a Markov generator matrix.

References

R. B. Israel et al.: Finding Generators for Markov Chains via Empirical Transition Matrices, with Applications to Credit Ratings. Mathematical Finance 11(2):245-265, 2001

Examples

## Derive matrix of relative transition frequencies
data(tm_abs)
tm_rel=rbind((tm_abs/rowSums(tm_abs))[1:7,],c(rep(0,7),1))

## Derive diagonal adjustment generator matrix estimate
gmda=gmDA(tm_rel,1)
gmda