DPOT: 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)
Value
VaR forecast and also MLE estimates of shape and time scale parameters.
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.
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.
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).
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 Unpublished article.