A Mixed Integer Linear Programming Approach to Markov Chain Bootstrapping

Bootstrapping time series is among the most acknowledged tools to study evolutive phenomena. In bootstrap procedures it is assumed that the phenomenon evolves according to a Markov chain. This does not apply when the process is continuous, as for economic and financial time series. In this paper we propose a method for bootstrapping time series defined over a continuous support. We discretize the support of the process and model it via a Markov chain of order k. We then formulate the problem of clustering similar rows in the original transition probability matrix as a Mixed Integer Linear Program and bootstrap series basing on the aggregated matrix. Medium size real-life instances are solved efficiently and preserving the characteristic features of the original series.