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A seasonal Markov model for extremely low temperatures
Author(s) -
Coles Stuart G.,
Tawn Jonathan A.,
Smith Richard L.
Publication year - 1994
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.3170050304
Subject(s) - extreme value theory , series (stratigraphy) , consistency (knowledge bases) , econometrics , term (time) , statistical physics , markov chain , markov process , relevance (law) , mathematics , environmental science , statistics , physics , geology , paleontology , geometry , quantum mechanics , political science , law
Abstract Time series of temperatures during periods of extreme cold display long‐term seasonal variability and short‐term temporal dependence. Classical approaches to extremes circumvent these issues, but in so doing cannot address questions relating to the temporal character of the process, though these issues are often the most important. In this paper a model is developed with the following features: periodic seasonal effects; consistency with asymptotic extreme value theory; Markov description of temporal dependence. Smith et al. studied the properties of such a model in the stationary case. Here, it is shown how such a model can be fitted to a non‐stationary series, and consequently used to estimate temporal aspects of the extremal process of low temperatures which have most practical and scientific relevance.