gmci {ctmcd}

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, ...)

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)

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.

Value

generator matrix confidence bounds

Author(s)

Marius Pfeuffer

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

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