# 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 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]