Integration

Julia code: click here.

# Julia code
# See A5.jl

Discretization of an AR(1) process

  1. Simulate a Markov chain
  2. Use Tauchen and Rouwenhorst’s to discretize
  3. Compute the first four moments
  4. Plot
Data Tauchen Tauchen Rouwenhorst Rouwenhorst
\(N = 5\) \(N = 15\) \(N = 5\) \(N = 15\)
\(mean\) \(-0.075\) \(-0.002\) \(0.049\) \(0.071\) \(0.08\)
\(var\) \(22.214\) \(13.94\) \(12.168\) \(20.772\) \(21.403\)
\(skew\) \(0.056\) \(-0.01\) \(-0.005\) \(0.021\) \(-0.042\)
\(kurt\) \(-0.13\) \(-0.981\) \(-0.998\) \(-0.491\) \(-0.191\)
\(acorr\) \(0.905\) \(0.84\) \(0.845\) \(0.898\) \(0.902\)
Density of Markov chainsDensity of Markov chains

Density of Markov chains

Application

  1. Discretize using Rouwenhorst’s
  2. Solve planner’s problem and plot
Solution plotSolution plot

Solution plot