Finite State Markov-Chain Approximations to Highly Persistent Processes

This paper re-examines the Rouwenhorst method of approximating first-order autoregressive processes. This method is appealing because it can match the conditional and unconditional mean, the conditional and unconditional variance and the first-order autocorrelation of any AR(1) process. This paper provides the first formal proof of this and other results. When comparing to five other methods, the Rouwenhorst method has the best performance in approximating the business cycle moments generated by the stochastic growth model. In addition, when the Rouwenhorst method is used, moments computed directly off the stationary distribution are as accurate as those obtained using Monte Carlo simulations.