intraCMM {AssetCorr}

Corrected Asymptotic Method of Moments Estimator of Frei and Wunsch (2018)

Description

The estimator is based on Frei and Wunsch (2018), who introduced an analytic bias correction via Taylor series expansion. Additionally, the bias due to autocorrelated default time series can be corrected. Furthermore, additional bootstrap and jackknife bias corrections are implemented.

Usage

intraCMM(d,n,l=0, B=0, DB=c(0,0), JC=FALSE , CI_Boot,type="bca", plot=FALSE)

Arguments

d

a vector, containing the default time series of the sector.

n

a vector, containing the number of obligors at the beginning of the period in the sector.

l

a number, indicating how many lags of autocorrelation should be used for the correction.

B

an integer, indicating how many bootstrap repetitions should be used for the single bootstrap corrected estimate.

DB

a combined vector, indicating how many bootstrap repetitions should be used for the inner (first entry) and outer loop (second entry) to correct the bias using the double bootstrap.

JC

a logical variable, indicating if the jackknife corrected estimate should be calculated.

CI_Boot

a number, indicating the desired confidence level if the single bootstrap correction is specified. By default, the interval is calculated as the bootstrap corrected and accelerated confidence interval (Bca).Furthermore, the analytical confidence intervals are provided, using the same value as CI_Boot.

type

a string, indicating the desired method to calculate the confidence intervals. For more details see boot.ci.

plot

a logical variable, indicating whether a plot of the single bootstrap density should be generated.

Details

Frei and Wunsch (2018) introduced an estimator which simultaneously corrects the bias of a short default time series and an bias due to autocorrelation. Additionally, further corrections are implemented. If DB is specified, the single bootstrap corrected estimate will be calculated by using the bootstrap values of the outer loop (oValues).

Value

The returned value is a list, containing the following components (depending on the selected arguments):

Original

Estimate of the original method

Bootstrap

Bootstrap corrected estimate

Double_Bootstrap

Double bootstrap corrected estimate

Jackknife

Jackknife corrected estimate

CI_Boot

Selected two-sided bootstrap confidence interval

bValues

Estimates from the single bootstrap resampling

iValues

Estimates from the double bootstrap resampling- inner loop

oValues

Estimates from the double bootstrap resampling- outer loop

References

Chang J, Hall P (2015). “Double-bootstrap methods that use a single double-bootstrap simulation.” Biometrika, 102(1), 203–214.

Efron B, Tibshirani RJ (1994). An introduction to the bootstrap. CRC press.

Frei C, Wunsch M (2018). “Moment Estimators for Autocorrelated Time Series and their Application to Default Correlations.” Journal of Credit Risk, 14, 1–29.

See Also

intraAMM, intraFMM, intraJDP2, intraMLE, intraJDP1, intraAMLE, intraMode,intraBeta

Examples

set.seed(10)
d=defaultTimeseries(1000,0.1,10,0.01)
n=rep(1000,10)

IntraCorr=intraCMM(d,n,l=0)


#Estimation with  two lags of autocorrelation
IntraCorr=intraCMM(d,n, l=2 )

#Jackknife correction
IntraCorr=intraCMM(d,n, JC=TRUE)




#Bootstrap correction with  bootstrap confidence intervals
IntraCorr=intraCMM(d,n, B=1000, CI_Boot=0.95 )

#Bootstrap correction with  bootstrap confidence intervals and plot
IntraCorr=intraCMM(d,n, B=1000, CI_Boot=0.95, plot=TRUE )

#Double Bootstrap correction with 10 repetitions in the inner loop and 50 in the outer loop
IntraCorr=intraCMM(d,n, DB=c(10,50))