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Inconsistency of the MLE and inference based on weighted LS for LARCH models

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  • Francq, Christian
  • Zakoïan, Jean-Michel

Abstract

This paper considers a class of finite-order autoregressive linear ARCH models. The model captures the leverage effect, allows the volatility to be arbitrarily close to zero and to reach its minimum for non-zero innovations, and is appropriate for long memory modeling when infinite orders are allowed. However, the (quasi-)maximum likelihood estimator is, in general, inconsistent. A self-weighted least-squares estimator is proposed and is shown to be asymptotically normal. A score test for conditional homoscedasticity and diagnostic portmanteau tests are developed. Their performance is illustrated via simulation experiments. It is also investigated whether stock market returns exhibit some of the characteristic features of the linear ARCH model.

Suggested Citation

  • Francq, Christian & Zakoïan, Jean-Michel, 2010. "Inconsistency of the MLE and inference based on weighted LS for LARCH models," Journal of Econometrics, Elsevier, vol. 159(1), pages 151-165, November.
    • Handle: RePEc:eee:econom:v:159:y:2010:i:1:p:151-165
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    Cited by:

    1. Jean-Michel Grandmont, 2016. "Endogenous Procyclicality of Labor Productivity, Employment, Real Wages and Effort in Conditionally Heteroskedastic Sunspots Unemployment Business Cycles with Negishi-Solow Efficiency Wages," Working Papers 2016:10, Department of Economics, University of Venice "Ca' Foscari".
    2. Jean-Michel Grandmont, "undated". "Countercyclical Endogenous Uncertainty Shocks, Efficiency Wages and Procyclical Precautionary Labor Productivity," Working Papers 2017:25, Department of Economics, University of Venice "Ca' Foscari".
    3. Mohamed Beraich & Karim Amzile & Jaouad Laamire & Omar Zirari & Mohamed Amine Fadali, 2022. "Volatility Spillover Effects of the US, European and Chinese Financial Markets in the Context of the Russia–Ukraine Conflict," IJFS, MDPI, vol. 10(4), pages 1-18, October.
    4. Francq, Christian & Wintenberger, Olivier & Zakoïan, Jean-Michel, 2013. "GARCH models without positivity constraints: Exponential or log GARCH?," Journal of Econometrics, Elsevier, vol. 177(1), pages 34-46.
    5. Bruno Milani & Paulo Sergio Ceretta, 2013. "Do Brazilian REITs depend on Real Estate sector companies or Overall Market?," Economics Bulletin, AccessEcon, vol. 33(4), pages 2948-2957.
    6. Jean-Michel Grandmont, 2016. "Endogenous Procyclicality of Labor Productivity, Employment, Real Wages and Effort in Conditionally Heteroskedastic Sunspots Unemployment Business Cycles with Negishi-Solow Efficiency Wages," Working Papers 2016-06, Center for Research in Economics and Statistics.
    7. Joanna Bruzda, 2020. "Multistep quantile forecasts for supply chain and logistics operations: bootstrapping, the GARCH model and quantile regression based approaches," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(1), pages 309-336, March.
    8. Feiyu Jiang & Dong Li & Ke Zhu, 2019. "Non-standard inference for augmented double autoregressive models with null volatility coefficients," Papers 1905.01798, arXiv.org.
    9. Jiang, Feiyu & Li, Dong & Zhu, Ke, 2020. "Non-standard inference for augmented double autoregressive models with null volatility coefficients," Journal of Econometrics, Elsevier, vol. 215(1), pages 165-183.
    10. Ieva Grublytė & Donatas Surgailis & Andrius Škarnulis, 2017. "QMLE for Quadratic ARCH Model with Long Memory," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(4), pages 535-551, July.
    11. Abdelhakim Aknouche & Eid Al-Eid, 2012. "Asymptotic inference of unstable periodic ARCH processes," Statistical Inference for Stochastic Processes, Springer, vol. 15(1), pages 61-79, April.
    12. Bardet, Jean-Marc & Doukhan, Paul & Wintenberger, Olivier, 2022. "Contrast estimation of time-varying infinite memory processes," Stochastic Processes and their Applications, Elsevier, vol. 152(C), pages 32-85.
    13. Marc Hallin & Davide La Vecchia, 2014. "Semiparametrically Efficient R-Estimation for Dynamic Location-Scale Models," Working Papers ECARES ECARES 2014-45, ULB -- Universite Libre de Bruxelles.
    14. Hallin, Marc & La Vecchia, Davide, 2017. "R-estimation in semiparametric dynamic location-scale models," Journal of Econometrics, Elsevier, vol. 196(2), pages 233-247.
    15. Jorge López Villa & Miriam Sosa Castro, 2021. "Contagio en la volatilidad entre los mercados de capital y de divisas en México y Brasil (2000-2020)," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 16(TNEA), pages 1-28, Septiembr.

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    More about this item

    Keywords

    Conditional homoscedasticity testing Leverage effect Linear ARCH Quasi-maximum likelihood Weighted least-squares;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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