A copula-based partition Markov procedure

ABSTRACTThe number of parameters needed to specify a discrete multivariate Markov chain grows exponentially with the order and dimension of the chain, and when the size of the database is not large enough, it is not possibly a consistent estimation. In this paper, we introduce a strategy to estimate a multivariate process with an order greater than the order achieved using standard procedures. The new strategy consists in obtaining a partition of the state space which is constructed from a combination of the partitions corresponding to the marginal processes and the partitions corresponding to the multivariate Markov chain.