# RPEGLMEN v1.0

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## Gamma and Exponential Generalized Linear Models with Elastic Net Penalty

Implements the fast iterative shrinkage-thresholding algorithm (FISTA) algorithm to fit a Gamma distribution with an elastic net penalty as described in Chen, Arakvin and Martin (2018) <arxiv:1804.07780>. An implementation for the case of the exponential distribution is also available, with details available in Chen and Martin (2018) <https://papers.ssrn.com/abstract_id=3085672>.

# RPEGLMEN

This package provides an implementation of the elastic net penalty for Gamma and exponentially distributed response variables.

### Installation

You can install the stable version on R CRAN.

install.packages("RPEGLMEN", dependencies = TRUE)


You can install the development version from GitHub.

library(devtools)
devtools::install_github("AnthonyChristidis/RPEGLMEN")


### Background Information

This package is designed to provide the user to fit an Exponential or Gamma distribution to the response variable with an elastic net penalty on the predictors. This package is of particular use in combination with the RPEIF and RPESE packages, in which the influence function of a time series of returns is used to compute the standard error of a risk and performance measure. See Chen and Martin (2018) for more details.

For the computational details to fit a Gamma distribution on data with an elastic net penalty, see Chen, Arakvin and Martin (2018).

### Usage

# Sample Code

library(RPEGLMEN)

# Function to return the periodogram of data series
myperiodogram <- function (data, max.freq = 0.5, twosided = FALSE, keep = 1){
data.fft <- fft(data)
N <- length(data)
tmp <- Mod(data.fft[2:floor(N/2)])^2/N
tmp <- sapply(tmp, function(x) max(1e-05, x))
freq <- ((1:(floor(N/2) - 1))/N)
tmp <- tmp[1:floor(length(tmp) * keep)]
freq <- freq[1:floor(length(freq) * keep)]
if (twosided) {
tmp <- c(rev(tmp), tmp)
freq <- c(-rev(freq), freq)
}
return(list(spec <- tmp, freq <- freq))
}

# Function to compute the standard error based the periodogram of the influence functions time series
SE.Gamma <- function(data, d = 7, alpha = 0.5, keep = 1, exponential.dist = TRUE){
N<-length(data)
# Compute the periodograms
my.periodogram <- myperiodogram(data)
my.freq <- my.periodogram$freq my.periodogram <- my.periodogram$spec
# Remove values of frequency 0 as it does not contain information about the variance
my.freq <- my.freq[-1]
my.periodogram <- my.periodogram[-1]
# Implement cut-off
nfreq <- length(my.freq)
my.freq <- my.freq[1:floor(nfreq*keep)]
my.periodogram <- my.periodogram[1:floor(nfreq*keep)]
# GLM with BFGS optimization
# Create 1, x, x^2, ..., x^d
x.mat <- rep(1,length(my.freq))
for(col.iter in 1:d){
x.mat <- cbind(x.mat,my.freq^col.iter)
}
# Fit the Exponential or Gamma model
if(exponential.dist)
res <- glmnet_exp(x.mat, my.periodogram, alpha.EN = alpha) else
res <- fit.glmGammaNet(x.mat, my.periodogram, alpha.EN = alpha)
# Return the estimated variance
return(sqrt(exp(res)/N))
}

data(edhec, package <- "PerformanceAnalytics")
colnames(edhec)

# Computing the expected shortfall for the time series of returns
library(RPEIF)
test.mat <- apply(edhec, 2, IF.ES)
test.mat <- apply(test.mat, 2, as.numeric)

# Returning the standard errors from the Exponential distribution fit
apply(test.mat, 2, SE.Gamma, exponential.dist = TRUE)


This package is free and open source software, licensed under GPL (>= 2).

## Functions in RPEGLMEN

 Name Description glmnet_exp Elastic Net Penalized Exponentially Distributed Response Variables fit.glmGammaNet Elastic Net Penalized Gamma or Exponentially Distributed Response Variables No Results!