78 research outputs found

    Approximating Markov Chains for Bootstrapping and Simulation

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    In this work we develop a bootstrap method based on the theory of Markov chains. The method moves from the two competing objectives that a researcher pursues when performing a bootstrap procedure: (i) to preserve the structural similarity -in statistical sense- between the original and the bootstrapped sample; (ii) to assure a diversification of the latter with respect to the former. The original sample is assumed to be driven by a Markov chain. The approach we follow is to implement an optimization problem to estimate the memory of a Markov chain (i.e. its order) and to identify its relevant states. The basic ingredients of the model are the transition probabilities, whose distance is measured through a suitably defined functional. We apply the method to the series of electricity prices in Spain. A comparison with the Variable Length Markov Chain bootstrap, which is a well established bootstrap method, shows the superiority of our proposal in reproducing the dependence among data

    A Tabu Search Heuristic Procedure in Markov Chain Bootstrapping

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    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 conrms the good consistency properties of the method we propose

    Kawasaki disease : an epidemiological study in central Italy

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    BACKGROUND: Kawasaki disease (KD) is a systemic vasculitis with an acute and self-limited course. The incidence of KD differs widely among ethnic groups and is higher in the Asian population. In Italy, no recent data are available. Our purpose is to define the epidemiology of Kawasaki disease in the years 2008-2013 in children aged\u2009<\u200914 years in the Italian regions of Tuscany and Emilia Romagna through administrative data. METHODS: We studied the epidemiology of KD in the years 2008-2013 in children 0-14 years old resident in Tuscany and in Emilia Romagna regions using hospital ICD-9 discharge codes with a thorough data cleaning for duplicates. RESULTS: The distribution of the KD patients across ages was similar for the two regions with a peak in the second year of life. When considering data of the two regions together, the rate of incidence was 17.6 for 100,000 children under 5 years. For both Regions the incidence rose slightly during the study period and had a seasonal distribution, with higher incidence in spring and winter. CONCLUSION: This is the first Italian study performed through the use of administrative data. Figures are in line but slightly higher than those published in other European countries

    The incorporation of fixed cost and multilevel capacities into the discrete and continuous single source capacitated facility location problem

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    In this study we investigate the single source location problem with the presence of several possible capacities and the opening (fixed) cost of a facility that is depended on the capacity used and the area where the facility is located. Mathematical models of the problem for both the discrete and the continuous cases using the Rectilinear and Euclidean distances are produced. Our aim is to find the optimal number of open facilities, their corresponding locations, and their respective capacities alongside the assignment of the customers to the open facilities in order to minimise the total fixed and transportation costs. For relatively large problems, two solution methods are proposed namely an iterative matheuristic approach and VNS-based matheuristic technique. Dataset from the literature is adapted to assess our proposed methods. To assess the performance of the proposed solution methods, the exact method is first applied to small size instances where optimal solutions can be identified or lower and upper bounds can be recorded. Results obtained by the proposed solution methods are also reported for the larger instances

    A Tabu Search heuristic procedure in Markov chain bootstrapping

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    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 conrms the good consistency properties of the method we propose

    Approximating multivariate Markov chains for bootstrapping through contiguous partitions

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    This paper extends Markov chain bootstrapping to the case of multivariate continuous-valued stochastic processes. To this purpose, we follow the approach of searching an optimal partition of the state space of an observed (multivariate) time series. The optimization problem is based on a distance indicator calculated on the transition probabilities of the Markov chain. Such criterion aims at grouping those states exhibiting similar transition probabilities. A second methodological contribution is represented by the addition of a contiguity constraint, which is introduced to force the states to group only if they have “near” values (in the state space). This requirement meets two important aspects: first, it allows a more intuitive interpretation of the results; second, it contributes to control the complexity of the problem, which explodes with the cardinality of the states. The computational complexity of the optimization problem is also addressed through the introduction of a novel Tabu Search algorithm, which improves both the quality of the solution found and the computing times with respect to a similar heuristic previously advanced in the literature. The bootstrap method is applied to two empirical cases: the bivariate process of prices and volumes of electricity in the Spanish market; the trivariate process composed of prices and volumes of a US company stock (McDonald’s) and prices of the Dow Jones Industrial Average index. In addition, the method is compared with two other well-established bootstrap methods. The results show the good distributional properties of the present proposal, as well as a clear superiority in reproducing the dependence among the data. This is a post-peer-review, pre-copyedit version of an article published in OR Spectrum. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00291-015-0397-
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