approximation¶
Filename: approximation.py
Authors: Thomas Sargent, John Stachurski
tauchen¶
Discretizes Gaussian linear AR(1) processes via Tauchen’s method

quantecon.markov.approximation.
tauchen
(rho, sigma_u, m=3, n=7)[source]¶ Computes the Markov matrix associated with a discretized version of the linear Gaussian AR(1) process
y_{t+1} = rho * y_t + u_{t+1}according to Tauchen’s method. Here {u_t} is an iid Gaussian process with zero mean.
Parameters: rho : scalar(float)
The autocorrelation coefficient
sigma_u : scalar(float)
The standard deviation of the random process
m : scalar(int), optional(default=3)
The number of standard deviations to approximate out to
n : scalar(int), optional(default=7)
The number of states to use in the approximation
Returns: x : array_like(float, ndim=1)
The state space of the discretized process
P : array_like(float, ndim=2)
The Markov transition matrix where P[i, j] is the probability of transitioning from x[i] to x[j]