Goodness-of-fit tests for parametric specifications of conditionally heteroscedastic models

Abstract

We consider a goodness-of-fit test for certain parametrizations of conditionally heteroscedastic time series with unobserved components. Our test is quite general in that it can be employed to validate any given specification of arbitrary order and may even be invoked for testing not just GARCH models but also some related models such as autoregressive conditional duration models. The test statistic utilizes the characterization of Bierens (J Econom 20:105–134, 1982) and may be written down in a convenient closed-form expression. Consistency of the test is proved, and the asymptotic distribution of the test statistic under the null hypothesis is studied. Since this distribution depends on unknown quantities, two bootstrap resampling schemes are investigated and compared in order to approximate critical points and actually carry out the test. Finite-sample results are presented as well as applications of the proposed procedures to real data from the financial markets.

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Acknowledgements

The authors are grateful to the anonymous referees for their constructive and useful comments. MD Jiménez-Gamero has been financially supported by Grant MTM2017–89422–P (Ministerio de Economía, Industria y Competitividad, Spain, and ERDF). S Lee has been supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT No. 2018R1A2A2A05019433. Part of the research of SG Meintanis was carried out at the Department of Economics and was supported by Grant Number 11699 of the Special Account for Research Grants (E\(\Lambda \)KE) of the National and Kapodistrian University of Athens.

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Correspondence to M. Dolores Jiménez-Gamero.

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Simos G. Meintanis: on sabbatical leave from the University of Athens.

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Jiménez-Gamero, M.D., Lee, S. & Meintanis, S.G. Goodness-of-fit tests for parametric specifications of conditionally heteroscedastic models. TEST 29, 682–703 (2020). https://doi.org/10.1007/s11749-019-00676-0

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Keywords

  • GARCH model
  • Goodness-of-fit test
  • Bierens characterization
  • Conditional duration model
  • Weighted bootstrap

Mathematics Subject Classification

  • 62G10
  • 62G20