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Properties of the Autocorrelation Function of Squared Observations for Second Order GARCH Processes under Two Sets of Parameter Constraints

Author

Listed:
  • He, Changli

    (Department of Economic Statistics)

  • Teräsvirta, Timo

    (Department of Economic Statistics)

Abstract

Nonnegativety constraints on the parameters of the GARCH (p, Q) model may be relaxed without giving up the requirement of the conditional variance remaining non- negative with probability one. This paper looks 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 nonnegative. The theory is illustrated by an empirical example.

Suggested Citation

  • He, Changli & Teräsvirta, Timo, 1997. "Properties of the Autocorrelation Function of Squared Observations for Second Order GARCH Processes under Two Sets of Parameter Constraints," SSE/EFI Working Paper Series in Economics and Finance 169, Stockholm School of Economics.
    • Handle: RePEc:hhs:hastef:0169
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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.

    More about this item

    Keywords

    Autoregressive conditional heteroskedasticity; conditional variance; fourth moment condition; time series; volatility;
    All these keywords.

    JEL classification:

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

    Statistics

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