RPEGLMEN (version 1.0)

fit.glmGammaNet: Elastic Net Penalized Gamma or Exponentially Distributed Response Variables

Description

git.glmGammaNet Fit glmnet model for Gamma distributed response data.

Usage

fit.glmGammaNet(A, b, exponential.dist = FALSE, alpha.EN = 0.5,
  num_lambda = 100L, glm_type = 1L, max_iter = 100L,
  abs_tol = 1e-04, rel_tol = 0.01, normalize_grad = FALSE,
  k_fold = 5L, has_intercept = TRUE, k_fold_iter = 5L,
  min.lambda.ratio = 1e-04, ...)

Arguments

A

The matrix of independent variables.

b

The vector of response variables.

exponential.dist

Parameter to determine whether we use the Exponential distribution (TRUE) or the Gamma distribution (FALSE).

alpha.EN

The coefficient of elastic net regularizer (1 means lasso).

num_lambda

Size of the lambda grid.

glm_type

Type of glm model, 1 is exponential, 2 is gamma (not implemented yet).

max_iter

Max number of iteration for the prox grad descent optimizer.

abs_tol

Absolute error threshold for the pgd optimizer.

rel_tol

Relative error threshold for the pgd optimizer (not used for vanilla PGD).

normalize_grad

Swtich for whether to normalize the gradient or not.

k_fold

The number of folds for cross validation.

has_intercept

Parameter to determine if there is an intercept (TRUE) or not (FALSE).

k_fold_iter

The number of iterations for the cross-validation.

min.lambda.ratio

Minimum lambda ratio for cross-validation.

...

Additional parameters.

Value

vector of optimal coefficient for the glm model.

Examples

# NOT RUN {
# 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
  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){
  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
  res <- fit.glmGammaNet(x.mat, my.periodogram, alpha.EN = alpha)
  # Return the estimated variance
  return(sqrt(exp(res[1])/N))
}

# Loading hedge fund data from PA
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 Gamma distribution fit
# apply(test.mat, 2, SE.Gamma)

# }

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