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Testing the tail index in autoregressive models

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Abstract

We propose a class of nonparametric tests on the Pareto tail index of the innovation distribution in the linear autoregressive model. The simulation study illustrates a good performance of the tests. Such tests have various applications in a study of flood flows, rainflow data, behavior of solids, atmospheric ozone layer and reliability analysis, in communication engineering, in stock markets and insurance.

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Authors and Affiliations

  1. Department of Probability and Mathematical Statistics, Charles University in Prague, Sokolovská 83, 186 75, Prague 8, Czech Republic

    Jana Jurečková

  2. Department of Statistics and Probability, Michigan State University, A413 Wells Hall, East Lansing, MI, 48824-1027, USA

    Hira L. Koul

  3. Department of Applied Mathematics, Technical University in Liberec, Hálkova 6, 461 17, Liberec 1, Czech Republic

    Jan Picek

Authors
  1. Jana Jurečková
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  2. Hira L. Koul
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  3. Jan Picek
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Corresponding author

Correspondence to Jana Jurečková.

Additional information

Research of J. Jurečková and J. Picek was partly supported by Czech Republic Grant 201/05/2340, by the Research Project LC06024 and by the NSF grant DMS 0071619. Research of H. L. Koul was partly supported by the NSF grants DMS 0071619 and 0704130.

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Jurečková, J., Koul, H.L. & Picek, J. Testing the tail index in autoregressive models. Ann Inst Stat Math 61, 579–598 (2009). https://doi.org/10.1007/s10463-007-0155-z

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  • DOI: https://doi.org/10.1007/s10463-007-0155-z

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