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Portmanteau test for the asymmetric power GARCH model when the power is unknown

Abstract

It is now widely accepted that, to model the dynamics of daily financial returns, volatility models have to incorporate the so-called leverage effect. We derive the asymptotic behaviour of the squared residuals autocovariances for the class of asymmetric power GARCH model when the power is unknown and is jointly estimated with the model’s parameters. We then deduce a portmanteau adequacy test based on the autocovariances of the squared residuals. These asymptotic results are illustrated by Monte Carlo experiments. An application to real financial data is also proposed.

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Acknowledgements

We sincerely thank the anonymous reviewers and editor for helpful remarks.

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Correspondence to Yacouba Boubacar Maïnassara.

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Boubacar Maïnassara, Y., Kadmiri, O. & Saussereau, B. Portmanteau test for the asymmetric power GARCH model when the power is unknown. Stat Papers (2021). https://doi.org/10.1007/s00362-021-01257-w

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Keywords

  • Asymmetric power GARCH models
  • Goodness-of-fit test
  • Portmanteau test
  • Residuals autocovariances
  • Threshold models
  • Validation

Mathematics Subject Classification

  • Primary 62M10
  • 62F03
  • 62F05
  • secondary 91B84
  • 62P05