gmvarkit (version 1.1.1)

calc_gradient: Calculate gradient or Hessian matrix

Description

calc_gradient or calc_hessian calculates the gradient or Hessian matrix of the given function at the given point using central difference numerical approximation. get_gradient or get_hessian calculates the gradient or Hessian matrix of the log-likelihood function at the parameter estimates of class 'gmvar' object. get_soc returns eigenvalues of the Hessian matrix.

Usage

calc_gradient(x, fn, h = 6e-06, ...)
calc_hessian(x, fn, h = 6e-06, ...)
get_gradient(gmvar, h = 6e-06)
get_hessian(gmvar, h = 6e-06)
get_soc(gmvar, h = 6e-06)

Arguments

x

a numeric vector specifying the point where the gradient or Hessian should be calculated.

fn

a function that takes in argument x as the first argument.

h

difference used to approximate the derivatives.

...

other arguments passed to fn

gmvar

object of class 'gmvar' created with fitGMVAR or GMVAR.

Value

Gradient functions return numerical approximation of the gradient, and Hessian functions return numerical approximation of the Hessian. get_soc returns eigenvalues of the Hessian matrix.

Warning

No argument checks!

Details

Especially the functions get_gradient or get_hessian can be used to check whether the found estimates denote a (local) maximum point, a saddle point or something else.

Examples

# NOT RUN {
  # Simple function
  foo <- function(x) x^2 + x
  calc_gradient(x=1, fn=foo)
  calc_gradient(x=-0.5, fn=foo)

  # More complicated function
  foo <- function(x, a, b) a*x[1]^2 - b*x[2]^2
  calc_gradient(x=c(1, 2), fn=foo, a=0.3, b=0.1)

  # These examples below use the data 'eurusd' which comes
  # with the package, but in a scaled form.
  data <- cbind(10*eurusd[,1], 100*eurusd[,2])
  colnames(data) <- colnames(eurusd)

  
# }
# NOT RUN {
  # GMVAR(1,2), d=2 model:
  params122 <- c(0.623, -0.129, 0.959, 0.089, -0.006, 1.006, 1.746,
    0.804, 5.804, 3.245, 7.913, 0.952, -0.037, -0.019, 0.943, 6.926,
    3.982, 12.135, 0.789)
  mod122 <- GMVAR(data, p=1, M=2, params=params122)
  get_gradient(mod122)
  get_hessian(mod122)
  get_soc(mod122)
  
# }