simulate_AR

subroutine simulate_AR(pi, shocks, fixed)

Description:

Simulates a time series of realizations from a discretized AR(1) process. Before being able to apply this simulation procedure, the process needs to be discretized into nodes and a transition matrix using the subroutine discretize_AR from the toolbox. The subroutine returns a series of indices that was draw according to the transition matrix . It thereby assumes that . To simulate the actual shock values, we just set .

Input arguments:

• integer :: pi(:, :)
  The transition matrix calculated with the subroutine discretize_AR . Note that this matrix needs to be a square matrix, the rows of which sum up to 1.

Output arguments:

• integer :: shocks(:)
  The subroutine stores the realizations of the time series in the one-dimensional array shocks. Note that the output values are of integer type, as they denote the indices of the respective discretization nodes.

Optional arguments:

• logical :: fixed
  If a logical variable fixed is passed to the subroutine that takes the value .true., the subroutine uses a fixed random seed. As a result, the sequence of random numbers drawn by the subroutine will always be the same every time your program is restarted. If fixed is not present or takes a value of .false., then the random seed is initialized at some arbitrary value that depends on the time and date at which you started your program. Hence, the series of random numbers drawn by this subroutine will be different every time your program is restarted.

References

• Parts of this routine were copied and adapted from:
  • The GNU gfortran compiler documentation for the initialization of the seed of the random number generator.
• For further reading refer to:
  • Toral, R. & Colet, P. (2014). Stochastic Numerical Methods: An Introduction for Students and Scientists. Weinheim: Wiley.
• 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