approximation

Filename: approximation.py

Authors: Thomas Sargent, John Stachurski

tauchen

Discretizes Gaussian linear AR(1) processes via Tauchen’s method

quantecon.markov.approximation.std_norm_cdf[source]
quantecon.markov.approximation.tauchen(rho, sigma_u, m=3, n=7)[source]

Computes a Markov chain associated with a discretized version of the linear Gaussian AR(1) process

y_{t+1} = rho * y_t + u_{t+1}

using 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:

mc : MarkovChain

An instance of the MarkovChain class that stores the transition matrix and state values returned by the discretization method