Bayesian estimation of an autoregressive model using Markov chain Monte Carlo

We present a complete Bayesian treatment of autoregressive model estimation incorporating choice of autoregressive order, enforcement of stationarity, treatment of outliers, and allowance for missing values and multiplicative seasonality. The paper makes three distinct contributions. First, we enforce the stationarity conditions using a very efficient Metropolis-within-Gibbs algorithm to generate the partial autocorrelations. Second we show how to carry out the Gibbs sampler when the autoregressive order is unknown. Third, we show how to combine the various aspects of fitting an autoregressive model giving a more comprehensive and efficient treatment than previous work. We illustrate our methodology with a real example.