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An ARCH Model Without Intercept

Author

Listed:
  • Christian M. HAFNER
  • Arie PREMINGER

Abstract

While theory of autoregressive conditional heteroskedasticity (ARCH) models is well understood for strictly stationary processes, some recent interest has focused on the nonstationary case. In the classical model including a positive intercept parameter, the volatility process diverges to infinity at least in probability, and it has been shown that no consistent estimator of the full parameter vector, including intercept, exists. This paper considers a nonstationary ARCH model which arises by setting the intercept term to zero. Unlike nonstationary ARCH models with positive intercept, this model includes the interesting case of log volatility following a random walk, which is called the stability case. For the ARCH(1) model without intercept, the paper derives asymptotic theory of the maximum likelihood estimator and proposes a test of the stability hypothesis. Numerical evidence illustrates the finite sample properties of the maximum likelihood estimator and the stability test.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Christian M. HAFNER & Arie PREMINGER, 2015. "An ARCH Model Without Intercept," LIDAM Reprints CORE 2770, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:2770
    Note: In : Economics Letters, 129, 13-17, 2015
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    Cited by:

    1. Li, Dong & Ling, Shiqing & Zhu, Ke, 2016. "ZD-GARCH model: a new way to study heteroscedasticity," MPRA Paper 68621, University Library of Munich, Germany.
    2. Yanlin Shi, 2023. "A simulation study on the Markov regime-switching zero-drift GARCH model," Annals of Operations Research, Springer, vol. 330(1), pages 1-20, November.
    3. Zhu, Ke, 2015. "Hausman tests for the error distribution in conditionally heteroskedastic models," MPRA Paper 66991, University Library of Munich, Germany.
    4. Zhu, Ke, 2023. "A new generalized exponentially weighted moving average quantile model and its statistical inference," Journal of Econometrics, Elsevier, vol. 237(1).
    5. Li, Dong & Zhang, Xingfa & Zhu, Ke & Ling, Shiqing, 2018. "The ZD-GARCH model: A new way to study heteroscedasticity," Journal of Econometrics, Elsevier, vol. 202(1), pages 1-17.
    6. Kejin Wu & Sayar Karmakar, 2021. "Model-Free Time-Aggregated Predictions for Econometric Datasets," Forecasting, MDPI, vol. 3(4), pages 1-14, December.

    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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