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Article overview
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Methods for estimating the upcrossings index: improvements ans comparison | Ana Paula Martins
; João Renato Sebastião
; | Date: |
1 Aug 2015 | Abstract: | The upcrossings index $0leq etaleq 1,$ a measure of the degree of local
dependence in the upcrossings of a high level by a stationary process, plays,
together with the extremal index $ heta,$ an important role in extreme events
modelling. For stationary processes, verifying a long range dependence
condition, upcrossings of high thresholds in different blocks can be assumed
asymptotically independent and therefore blocks estimators for the upcrossings
index can be easily constructed using disjoint blocks. In this paper we focus
on the estimation of the upcrossings index via the blocks method and properties
such as consistency and asymptotic normality are studied. We also enlarge the
family of runs estimators of $eta$ and provide an empirical way of checking
local dependence conditions that control the clustering of upcrossings to
improve the estimates obtained with the runs method.
We compare the performance of a range of different estimators for $eta$ and
illustrate the methods using simulated data and financial data. | Source: | arXiv, 1508.0053 | Services: | Forum | Review | PDF | Favorites |
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