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Extremes of Markov chains with tail switching potential
Author(s) -
Bortot Paola,
Coles Stuart
Publication year - 2003
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1046/j.1369-7412.2003.00419.x
Subject(s) - markov chain , heteroscedasticity , autoregressive model , series (stratigraphy) , econometrics , variable order markov model , markov process , extreme value theory , markov property , markov model , compendium , computer science , mathematics , statistical physics , statistics , physics , paleontology , archaeology , biology , history
Summary. A recent advance in the utility of extreme value techniques has been the characteri‐ zation of the extremal behaviour of Markov chains. This has enabled the application of extreme value models to series whose temporal dependence is Markovian, subject to a limitation that prevents switching between extremely high and extremely low levels. For many applications this is sufficient, but for others, most notably in the field of finance, it is common to find series in which successive values switch between high and low levels. We term such series Markov chains with tail switching potential, and the scope of this paper is to generalize the previous theory to enable the characterization of the extremal properties of series displaying this type of behaviour. In addition to theoretical developments, a modelling procedure is proposed. A simulation study is made to assess the utility of the model in inferring the extremal dependence structure of autoregressive conditional heteroscedastic processes, which fall within the tail switching Markov family, and generalized autoregressive conditional heteroscedastic processes which do not, being non‐Markov in general. Finally, the procedure is applied to model extremal aspects of a financial index extracted from the New York Stock Exchange compendium.