A New Dependence Condition for Time Series and the Extremal Index of Higher-Order Markov Chains
We present a new dependence condition for time series and extend the extremal types theorem. The dependence structure of a stationary sequence is described by a sequence of extremal functions. Under a stability condition for the sequence of extremal functions, we obtain the asymptotic distribution...
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| Format: | Article |
| Language: | English |
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Instituto Nacional de Estatística | Statistics Portugal
2006-06-01
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| Series: | Revstat Statistical Journal |
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| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/32 |
| _version_ | 1828452719566782464 |
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| author | Helena Ferreira |
| author_facet | Helena Ferreira |
| author_sort | Helena Ferreira |
| collection | DOAJ |
| description |
We present a new dependence condition for time series and extend the extremal types theorem. The dependence structure of a stationary sequence is described by a sequence of extremal functions. Under a stability condition for the sequence of extremal functions, we obtain the asymptotic distribution of the sample maximum. As a corollary, we derive a surprisingly simple method for computing the extremal index through a limit of a sequence of extremal coefficients. The results may be used to determine the asymptotic distribution of extreme values from stationary time series based on copulas. We illustrate it with the study of the extremal behaviour of d th-order stationary Markov chains in discrete time with continuous state space. For such sequences we present a way to compute the extremal index from the upper extreme value limit for its joint distribution of d + 1 consecutive variables.
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| first_indexed | 2024-12-10T23:56:56Z |
| format | Article |
| id | doaj.art-58accaed1d46414b9a46aa3cb469f322 |
| institution | Directory Open Access Journal |
| issn | 1645-6726 2183-0371 |
| language | English |
| last_indexed | 2024-12-10T23:56:56Z |
| publishDate | 2006-06-01 |
| publisher | Instituto Nacional de Estatística | Statistics Portugal |
| record_format | Article |
| series | Revstat Statistical Journal |
| spelling | doaj.art-58accaed1d46414b9a46aa3cb469f3222022-12-22T01:28:34ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712006-06-014210.57805/revstat.v4i2.32A New Dependence Condition for Time Series and the Extremal Index of Higher-Order Markov ChainsHelena Ferreira 0University of Beira Interior We present a new dependence condition for time series and extend the extremal types theorem. The dependence structure of a stationary sequence is described by a sequence of extremal functions. Under a stability condition for the sequence of extremal functions, we obtain the asymptotic distribution of the sample maximum. As a corollary, we derive a surprisingly simple method for computing the extremal index through a limit of a sequence of extremal coefficients. The results may be used to determine the asymptotic distribution of extreme values from stationary time series based on copulas. We illustrate it with the study of the extremal behaviour of d th-order stationary Markov chains in discrete time with continuous state space. For such sequences we present a way to compute the extremal index from the upper extreme value limit for its joint distribution of d + 1 consecutive variables. https://revstat.ine.pt/index.php/REVSTAT/article/view/32extremal coefficientdependenceextremesextremal indexhigher-order stationary Markov sequences |
| spellingShingle | Helena Ferreira A New Dependence Condition for Time Series and the Extremal Index of Higher-Order Markov Chains Revstat Statistical Journal extremal coefficient dependence extremes extremal index higher-order stationary Markov sequences |
| title | A New Dependence Condition for Time Series and the Extremal Index of Higher-Order Markov Chains |
| title_full | A New Dependence Condition for Time Series and the Extremal Index of Higher-Order Markov Chains |
| title_fullStr | A New Dependence Condition for Time Series and the Extremal Index of Higher-Order Markov Chains |
| title_full_unstemmed | A New Dependence Condition for Time Series and the Extremal Index of Higher-Order Markov Chains |
| title_short | A New Dependence Condition for Time Series and the Extremal Index of Higher-Order Markov Chains |
| title_sort | new dependence condition for time series and the extremal index of higher order markov chains |
| topic | extremal coefficient dependence extremes extremal index higher-order stationary Markov sequences |
| url | https://revstat.ine.pt/index.php/REVSTAT/article/view/32 |
| work_keys_str_mv | AT helenaferreira anewdependenceconditionfortimeseriesandtheextremalindexofhigherordermarkovchains AT helenaferreira newdependenceconditionfortimeseriesandtheextremalindexofhigherordermarkovchains |