DPOT {evt0}

Duration based peaks over threshold value-at-risk forecast

Description

This function calculate the value-at-risk (VaR) forecast for the durations-based peaks over threshold (DPOT) models.

Usage

DPOT(x, cov=0.01, c=0.75, th=0.1,  nd=1000)

Arguments

x

Data vector.

cov

Coverage value, default is cov=0.01.

c

Tuning parameter, default is c=0.75.

th

Threshold value, default is th=0.1.

nd

Returns days, default is nd=1000.

Details

In financial time series a relation between the excesses and the durations between excesses is usuallly observed. Araujo Santos and Fraga Alves (2013) propose using this dependece to improve the risk forecasts with DPOT models. The computation method in DPOT() function is based on the work from Araujo Santos and Fraga Alves (2012).

Value

VaR forecast and also MLE estimates of shape and time scale parameters.

Warning

After running the function following message appears: In log(1+gamma*y/(alpha1*(1/x)^c )): NaNs produced when the gamma is negative but the optimizer continue to other iternations choosing other values until it converge.

Author(s)

P. Araujo Santos [e-mail], M.I. Fraga Alves [e-mail]

References

Araujo Santos, P. and Fraga Alves, M.I. (2013). Forecasting Value-at-Risk with a duration-based POT method. Mathematics and Computers in Simulation, 94, 295–309.

Araujo Santos, P. and Fraga Alves, M.I. (2012). R Program to Implement the DPOT Model. Unpublished article.

Examples

#Read S&P500 from data file
data(S_P500)
str(S_P500)

# One day ahead VaR forecast
DPOT(S_P500$returns,0.01,0.75,0.1,1000)