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Properties of the Autocorrelation Function of Squared Observations for Second‐order Garch Processes Under Two Sets of Parameter Constraints

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  • Changli He
  • Timo Terasvirta

Abstract

Non‐negativity constraints on the parameters of the GARCH(p, q) process may be relaxed without giving up the requirement that the conditional variance remains non‐negative with probability 1. In this paper we look into the consequences of adopting these less severe constraints in the GARCH(2, 2) case and its two second‐order special cases, GARCH(2, 1) and GARCH(1, 2). This is done by comparing the autocorrelation function of squared observations under these two sets of constraints. The less severe constraints allow more flexibility in the shape of the autocorrelation function than the constraints restricting the parameters to be non‐negative.

Suggested Citation

  • Changli He & Timo Terasvirta, 1999. "Properties of the Autocorrelation Function of Squared Observations for Second‐order Garch Processes Under Two Sets of Parameter Constraints," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(1), pages 23-30, January.
    • Handle: RePEc:bla:jtsera:v:20:y:1999:i:1:p:23-30
    DOI: 10.1111/1467-9892.00123
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    Cited by:

    1. Doornik, Jurgen A. & Ooms, Marius, 2008. "Multimodality in GARCH regression models," International Journal of Forecasting, Elsevier, vol. 24(3), pages 432-448.
    2. Georgios Bampinas & Konstantinos Ladopoulos & Theodore Panagiotidis, 2018. "A note on the estimated GARCH coefficients from the S&P1500 universe," Applied Economics, Taylor & Francis Journals, vol. 50(34-35), pages 3647-3653, July.
    3. Feng, Yuanhua & Beran, Jan & Yu, Keming, 2006. "Modelling financial time series with SEMIFAR-GARCH model," MPRA Paper 1593, University Library of Munich, Germany.

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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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