Binomial Autoregressive Moving Average Models with an Application to U.S. Recessions

Binary Autoregressive Moving Average (BARMA) models provide a modeling technology for binary time series analogous to the classic Gaussian ARMA models used for continuous data. BARMA models mitigate the curse of dimensionality found in long lag Markov models and allow for non-Markovian persistence. The autopersistence function (APF) and autopersistence graph (APG) provide analogs to the autocorrelation function and correlogram. Parameters of the BARMA model may be estimated by either maximum likelihood or MCMC methods. Application of the BARMA model to U.S. recession data suggests that a BARMA(2,2) model is superior to traditional Markov models.