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.
A Mixed Integer Linear Programming Approach to Markov Chain Bootstrapping / Cerqueti, R.; Falbo, P.; Pelizzari, C.; Ricca, Federica; Scozzari, A.. - STAMPA. - Università degli Studi di Macerata, Dipartimento di Economia e Diritto, Quaderno di Dipartimento n. 67:(2012).
A Mixed Integer Linear Programming Approach to Markov Chain Bootstrapping
R. Cerqueti;RICCA, Federica;
2012
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.