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Statistical Inference For Measurement Equation Selection In The Log-Realgarch Model

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  • Li, Yu-Ning
  • Zhang, Yi
  • Zhang, Caiya

Abstract

This article investigates the statistical inference problem of whether a measurement equation is self-consistent in the logarithmic realized GARCH model (log-RealGARCH). First, we provide the sufficient and necessary conditions for the strict stationarity of both the log-RealGARCH model and the log-GARCH-X model. Under these conditions, strong consistency and asymptotic normality of the quasi-maximum likelihood estimators of these two models are obtained. Then, based on the asymptotic results, we propose a Hausman-type self-consistency test for diagnosing the suitability of the measurement equation in the log-RealGARCH model. Finally, the results of simulations and an empirical study are found to accord with the theoretical results.

Suggested Citation

  • Li, Yu-Ning & Zhang, Yi & Zhang, Caiya, 2019. "Statistical Inference For Measurement Equation Selection In The Log-Realgarch Model," Econometric Theory, Cambridge University Press, vol. 35(5), pages 943-977, October.
    • Handle: RePEc:cup:etheor:v:35:y:2019:i:05:p:943-977_00
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    Cited by:

    1. Antonio Naimoli & Giuseppe Storti, 2021. "Forecasting Volatility and Tail Risk in Electricity Markets," JRFM, MDPI, vol. 14(7), pages 1-17, June.
    2. Stavroula Yfanti & Georgios Chortareas & Menelaos Karanasos & Emmanouil Noikokyris, 2022. "A three‐dimensional asymmetric power HEAVY model," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(3), pages 2737-2761, July.
    3. Naimoli, Antonio, 2022. "The information content of sentiment indices for forecasting Value at Risk and Expected Shortfall in equity markets," MPRA Paper 112588, University Library of Munich, Germany.
    4. Naimoli, Antonio & Gerlach, Richard & Storti, Giuseppe, 2022. "Improving the accuracy of tail risk forecasting models by combining several realized volatility estimators," Economic Modelling, Elsevier, vol. 107(C).

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