Here is my implementation of Martin Floden's matlab code for the routine.

Click here to download the script.

```
```

```
import scipy.stats as st
import scipy as sp
def tauchenhussey(N,mu,rho,sigma, baseSigma):
"""
Function tauchenhussey
Purpose: Finds a Markov chain whose sample paths
approximate those of the AR(1) process
z(t+1) = (1-rho)*mu + rho * z(t) + eps(t+1)
where eps are normal with stddev sigma
Format: {Z, Zprob} = TauchenHussey(N,mu,rho,sigma,m)
Input: N scalar, number of nodes for Z
mu scalar, unconditional mean of process
rho scalar
sigma scalar, std. dev. of epsilons
baseSigma scalar, std. dev. used to calculate Gaussian
quadrature weights and nodes, i.e. to build the
grid. I recommend that you use
baseSigma = w*sigma +(1-w)*sigmaZ where sigmaZ = sigma/sqrt(1-rho^2),
and w = 0.5 + rho/4. Tauchen & Hussey recommend
baseSigma = sigma, and also mention baseSigma = sigmaZ.
Output: Z N*1 vector, nodes for Z
Zprob N*N matrix, transition probabilities
Author: Benjamin Tengelsen, Carnegie Mellon University (python)
Martin Floden, Stockholm School of Economics (original)
January 2007 (updated August 2007)
This procedure is an implementation of Tauchen and Hussey's
algorithm, Econometrica (1991, Vol. 59(2), pp. 371-396)
"""
Z = sp.zeros((N,1))
Zprob = sp.zeros((N,N))
[Z,w] = gaussnorm(N,mu,baseSigma**2)
for i in range(N):
for j in range(N):
EZprime = (1-rho)*mu + rho*Z[i]
Zprob[i,j] = w[j] * st.norm.pdf(Z[j],EZprime,sigma) / st.norm.pdf(Z[j],mu,baseSigma)
for i in range(N):
Zprob[i,:] = Zprob[i,:] / sum(Zprob[i,:])
return Z.T,Zprob
def gaussnorm(n,mu,s2):
"""
Find Gaussian nodes and weights for the normal distribution
n = # nodes
mu = mean
s2 = variance
"""
[x0,w0] = gausshermite(n)
x = x0*sp.sqrt(2.*s2) + mu
print s2,mu
print x
w = w0/sp.sqrt(sp.pi)
return [x,w]
def gausshermite(n):
"""
Gauss Hermite nodes and weights following 'Numerical Recipes for C'
"""
MAXIT = 10
EPS = 3e-14
PIM4 = 0.7511255444649425
x = sp.zeros((n,1))
w = sp.zeros((n,1))
m = int((n+1)/2)
for i in range(m):
if i == 0:
z = sp.sqrt((2.*n+1)-1.85575*(2.*n+1)**(-0.16667))
elif i == 1:
z = z - 1.14*(n**0.426)/z
elif i == 2:
z = 1.86*z - 0.86*x[0]
elif i == 3:
z = 1.91*z - 0.91*x[1]
else:
z = 2*z - x[i-1]
for iter in range(MAXIT):
p1 = PIM4
p2 = 0.
for j in range(n):
p3 = p2
p2 = p1
p1 = z*sp.sqrt(2./(j+1))*p2 - sp.sqrt(float(j)/(j+1))*p3
pp = sp.sqrt(2.*n)*p2
z1 = z
z = z1 - p1/pp
if sp.absolute(z-z1) <= EPS:
break
if iter>MAXIT:
error('too many iterations'), end
x[i,0] = z
x[n-i-1,0] = -z
w[i,0] = 2./pp/pp
w[n-i-1,0] = w[i]
x = x[::-1]
return [x,w]
```

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