discretize_AR - fabiankindermann/ce-fortran GitHub Wiki

subroutine discretize_AR(rho, mu, sigma_eps, z, pi, w)

This subroutine calculates the nodes , transition matrix , and weights for an approximation of an AR(1) process with normally distributed innovations of the type

The process features an autocorrelation coefficient , an unconditional mean of and a variance of the innovation of . The unconditional variance of is .

We can use the nodes and weights, for example, to calculate unconditional moments as

The conditional moments can be calculated from

This subroutine uses the Rouwenhorst method to discretize the stochastic process.

• real*8 :: rho
  A scalar indicating the autocorrelation coefficient . This input value needs to be an element of the interval .
• real*8 :: mu
  A scalar indicating the unconditional mean .
• real*8 :: sigma_eps
  A scalar indicating the variance of the innovation term . This input value can not be smaller than zero.

• real*8 :: z(:)
  A one-dimensional array into which the subroutine stores the approximation nodes .
• real*8 :: pi(:, :)
  A two-dimensional array into which the subroutine stores the transition matrix . Note that along each dimension, pi needs to have the same length as z.

• real*8 :: w(:)
  A one-dimensional array into which the subroutine stores the weights of the unconditional distribution. Note that w needs to have the same length as z.

• For further reading refer to:
  • Kopecky, K.A. & Suen, R.M.H. (2010). Finite state Markov-chain approximations to highly persistent processes. Review of Economic Dynamics, 13(3), 701-714.
  • Rouwenhorst, K.G. (1995). Asset pricing implications of equilibrium business cycle models. in: Cooley, T.F. (Ed.), Frontiers in Business Cycle Research, Princeton: Princeton University Press, 294-330.
• This routine is used in the following programs:
  • prog09_03.f90
  • prog09_04.f90
  • prog09_05.f90
  • prog09_06.f90
  • prog09_07.f90
  • prog09_08.f90
  • prog09_09.f90
  • prog09_10.f90
  • prog10_01.f90
  • prog10_02.f90
  • prog10_03.f90
  • prog10_01.f90
  • prog11_02.f90
  • prog11_03.f90