© 1998 by Biometrika Trust
Models for the extremes of Markov chains
Department of Statistical Sciences, University of Padova 35121 Padova, Italybortot{at}hal.stat.unipd.it
Department of Mathematics and Statistics, Lancaster University University, Lancaster LA1 4YF, U.K.j.tawn{at}lancaster.ac.uk
The modelling of extremes of a time series has progressed from the assumption of independent observations to more realistic forms of temporal dependence. In this paper, we focus on Markov chains, deriving a class of models for their joint tail which allows the degree of clustering of extremes to decrease at high levels, overcoming a key Limitation in current methodologies. Theoretical aspects of the model are examined and a simulation algorithm is developed through which the stochastic properties of summaries of the extremal txhaviour of the chain are evaluated. The approach is illustrated through a simulation study of extremal events of Gaussian autoregressive processes and an application to temperature data.
Key Words: Asymptotic independence • Bivariate extreme value distribution • Extremal index • Extreme value theory • Gaussian process • Markov chain
CiteULike 
Connotea 
Del.icio.us What's this?
This article has been cited by other articles:
|
|
 |
|
  B. V. Mendes and A. R. Moretti Improving financial risk assessment through dependency Statistical Modeling, July 1, 2002; 2(2): 103 - 122. [Abstract] [PDF]
|
|