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IMA Journal of Management Mathematics Advance Access published online on October 8, 2007
IMA Journal of Management Mathematics, doi:10.1093/imaman/dpm026
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© The authors 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Hidden Markov models for scenario generation

Enza Messina{dagger}

DISCO (Dipartimento di Informatica Sistemistica e COmunicazione), University of Milano Bicocca, Via Bicocca degli Arcimboldi, 8, 20126 Milano, Italy

Daniele Toscani{ddagger}

DISCO (Dipartimento di Informatica Sistemistica e COmunicazione), University of Milano Bicocca, Via Bicocca degli Arcimboldi 8, 20126 Milano, Italy and Consorzio Milano Ricerche, Via Cicognara 7, 20129 Milano, Italy

{dagger} Email: messina{at}disco.unimib.it

{ddagger} Email: toscani{at}milanoricerche.it

We consider the problem of modelling processes sequentially changing behaviour and unexpected changes that can hinder finding the best approximation function. These dynamics cannot be observed directly either because they are masked by observational noise or because the process generating them is too complex and involves too many variables. In this paper, the problem of modelling financial time series has been approached using hidden Markov models (HMMs), which have been shown to be suitable for sequential data analysis and in particular for financial time series modelling and forecasting. HMMs are essentially data-driven models that allow us to focus attention on the observation generation process, which is indeed final objective. The goal of our time series analysis model is the generation of scenarios to be included in decision models. Therefore, our focus will not be on determining the best forecast but in capturing the generation process behaviour in order to characterize its possible evolutions.

Keywords: scenario generation; simulation; hidden Markov models


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