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]