A Tabu Search heuristic procedure in Markov chain bootstrapping

Markov chain theory is proving to be a powerful approach to bootstrap ?nite 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 the state space of a continuous-valued process into a ?nite number of intervals or unions of intervals (i.e. its states) and identify the time lags which provide \memory" to the process. A distance is used as objective function to stimulate the clustering of the states having similar transition probabilities. The problem of the exploding number of alternative partitions in the solution space (which grows with the number of states and the order of the Markov chain) is addressed through a Tabu Search algorithm. The method is applied to bootstrap the series of the German and Spanish electricity prices. The analysis of the results con?rms the good consistency properties of the method we propose.