ctmcd (version 1.4.4)

gmci: Confidence / Credibility Intervals for Generator Matrix Objects

Description

Generic function to derive confidence / credibility intervals for "EM" or "GS" based generator matrix objects

Usage

gmci(gm, alpha, ...)

Value

generator matrix confidence bounds

Arguments

gm

a "EM" or "GS" generator matrix object

alpha

significance level

...

additional arguments:

• eps: threshold for which generator matrix parameters are assumed to be fixed at zero (if "EM" object)

• cimethod: "Direct" and "SdR" use analytical expressions of the Fisher information matrix, "BS" employs the numerical approach of Bladt and Soerensen, 2009 (if "EM" object)

• expmethod: method to compute matrix exponentials (see ?expm from expm package for more information)

Author

Marius Pfeuffer

Details

If gm is based on the "EM" method (expectation-maximization algorithm), the function computes a Wald confidence interval based on the method of Oakes, 1999. IF gm is based on the "GS" method (Gibbs sampler), the function computes an equal-tailed credibility interval.

References

M. Bladt and M. Soerensen. Efficient Estimation of Transition Rates Between Credit Ratings from Observations at Discrete Time Points. Quantitative Finance, 9(2):147-160, 2009

D. Oakes. Direct calculation of the information matrix via the EM algorithm. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 61(2):479-482, 1999

G. Smith and G. dos Reis. Robust and Consistent Estimation of Generators in Credit Risk. Quantitative Finance 18(6):983-1001, 2018

G. dos Reis, M. Pfeuffer, G. Smith: Capturing Rating Momentum in the Estimation of Probabilities of Default, With Application to Credit Rating Migrations (In Preparation), 2018

Examples

# \donttest{
data(tm_abs)

## Maximum Likelihood Generator Matrix Estimate
gm0=matrix(1,8,8)
diag(gm0)=0
diag(gm0)=-rowSums(gm0)
gm0[8,]=0

gmem=gm(tm_abs,te=1,method="EM",gmguess=gm0)

## Oakes Confidence Interval
ciem=gmci(gmem,alpha=0.05)
ciem
# }