Penalised likelihood methods for phase-type dimension selection

Albrecher Hansjörg (), Bladt Martin () and Müller Alaric J. A. ()
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Albrecher Hansjörg: Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, UNIL-Dorigny; and Swiss Finance Institute, 1015 Lausanne Switzerland
Bladt Martin: Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, UNIL-Dorigny, 1015 Lausanne Switzerland
Müller Alaric J. A.: Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, UNIL-Dorigny, 1015 Lausanne Switzerland

Statistics & Risk Modeling, 2022, vol. 39, issue 3-4, 75-92

Abstract: Phase-type distributions are dense in the class of distributions on the positive real line, and their flexibility and closed-form formulas in terms of matrix calculus allow fitting models to data in various application areas. However, the parameters are in general non-identifiable, and hence the dimension of two similar models may be very different. This paper proposes a new method for selecting the dimension of phase-type distributions via penalisation of the likelihood function. The penalties are in terms of the Green matrix, from which it is possible to extract the contributions of each state to the overall mean. Since representations with higher dimensions are penalised, a parsimony effect is obtained. We perform a numerical study with randomly generated phase-type samples to illustrate the effectiveness of the proposed procedure, and also apply the technique to the absolute log-returns of EURO STOXX 50 and Bitcoin prices.

Keywords: Phase-type distributions; maximum likelihood estimation; dimension selection; transformation via rewards (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1515/strm-2021-0026

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