tmci: Delta Method Confidence Intervals for Matrix Exponential...

In ctmcd: Estimating the Parameters of a Continuous-Time Markov Chain from Discrete-Time Data

Delta Method Confidence Intervals for Matrix Exponential Transformations of Generator Matrix Objects

Description

Generic function to derive delta method based confidence intervals for matrix exponential transformations of "EM" based generator matrix objects

Usage

tmci(gmem, alpha, te, eps = 1e-04, expmethod = "PadeRBS")

Arguments

gmem	an "EM" generator matrix object
alpha	significance level
te	discrete time horizon for which the interval is supposed to be computed
eps	threshold for which generator matrix parameters are assumed to be fixed at zero
expmethod	method to compute matrix exponentials (see ?expm from expm package for more information)

Details

Confidence intervals for discrete-time transition matrix predictions given generator matrix estimates are computed by using the delta method for matrix exponential transformations.

Value

transition matrix confidence bounds

References

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)

## 2.5 Year Transition Matrix Confidence Interval
citm=tmci(gmem,alpha=0.05,te=2.5)
citm

ctmcd documentation built on May 31, 2023, 7:55 p.m.