Markov chain theory is proving to be a powerful approach to bootstrap highly nonlinear time series. In this work we provide a method to estimate the memory of a Markov chain (i.e. its order) and to identify its relevant states. In particular the choice of memory lags and the aggregation of...

Bootstrapping time series is one of the most acknowledged tools to make forecasts and study the statistical properties of an evolutive phenomenon. The idea underlying this procedure is to replicate the phenomenon on the basis of an observed sample. One of the most important classes of bootstrap...

Markov chain theory is proving to be a powerful approach to bootstrap finite states processes, especially where time dependence is non linear. In this work we extend such approach to bootstrap discrete time continuous-valued processes. To this purpose we solve a minimization problem to partition...

 <font size="1">While the large portion of the literature on Markov chain (possibly of orderhigher than one) bootstrap methods has focused on the correct estimation ofthe transition probabilities, little or no attention has been devoted to theproblem of estimating the dimension of the transition probability...</font>