Determining and interpreting the order of a two-state Markov Chain: Application to models of daily precipitation

Lumping together some of the states of a many-state first-order Markov chain does not in general give a first-order Markov chain with a smaller number of states. If a series generated in this way is nevertheless assumed to have been produced by a two-state Markov chain, standard statistical procedures (using the Akaike and Bayesian information criteria) may indicate that it should be fitted by a higher order than first. Stochastic models based on a Markov chain are often used to model precipitation series. It is normal to classify days as "dry' and "wet' and fit a two-state process. In some cases, second- or higher-order chains are preferred by reference to information criteria. This might be because a many-state process, possibly of only first order, would actually be a better choice than a two-state process.