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Testing Garch-X Type Models

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  • Pedersen, Rasmus Søndergaard
  • Rahbek, Anders

Abstract

We present novel theory for testing for reduction of GARCH-X type models with an exogenous (X) covariate to standard GARCH type models. To deal with the problems of potential nuisance parameters on the boundary of the parameter space as well as lack of identification under the null, we exploit a noticeable property of specific zero-entries in the inverse information of the GARCH-X type models. Specifically, we consider sequential testing based on two likelihood ratio tests and as demonstrated the structure of the inverse information implies that the proposed test neither depends on whether the nuisance parameters lie on the boundary of the parameter space, nor on lack of identification. Asymptotic theory is derived essentially under stationarity and ergodicity, coupled with a regularity assumption on the exogenous covariate X. Our general results on GARCH-X type models are applied to Gaussian based GARCH-X models, GARCH-X models with Student’s t-distributed innovations as well as integer-valued GARCH-X (PAR-X) models.

Suggested Citation

  • Pedersen, Rasmus Søndergaard & Rahbek, Anders, 2019. "Testing Garch-X Type Models," Econometric Theory, Cambridge University Press, vol. 35(5), pages 1012-1047, October.
    • Handle: RePEc:cup:etheor:v:35:y:2019:i:05:p:1012-1047_00
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    Cited by:

    1. Gregory Fletcher Cox, 2024. "A Simple and Adaptive Confidence Interval when Nuisance Parameters Satisfy an Inequality," Papers 2409.09962, arXiv.org.
    2. Francisco Blasques & Christian Francq & Sébastien Laurent, 2020. "A New Class of Robust Observation-Driven Models," Tinbergen Institute Discussion Papers 20-073/III, Tinbergen Institute.
    3. Blasques, F. & Francq, Christian & Laurent, Sébastien, 2023. "Quasi score-driven models," Journal of Econometrics, Elsevier, vol. 234(1), pages 251-275.
    4. Cavaliere, Giuseppe & Nielsen, Heino Bohn & Pedersen, Rasmus Søndergaard & Rahbek, Anders, 2022. "Bootstrap inference on the boundary of the parameter space, with application to conditional volatility models," Journal of Econometrics, Elsevier, vol. 227(1), pages 241-263.
    5. Rémy Garnier, 2022. "Concurrent neural network: a model of competition between times series," Annals of Operations Research, Springer, vol. 313(2), pages 945-964, June.
    6. Hetland, Simon & Pedersen, Rasmus Søndergaard & Rahbek, Anders, 2023. "Dynamic conditional eigenvalue GARCH," Journal of Econometrics, Elsevier, vol. 237(2).
    7. Yao, Yuan & Zhao, Yang & Li, Yan, 2022. "A volatility model based on adaptive expectations: An improvement on the rational expectations model," International Review of Financial Analysis, Elsevier, vol. 82(C).
    8. M. Karanasos & S. Yfanti & J. Hunter, 2022. "Emerging stock market volatility and economic fundamentals: the importance of US uncertainty spillovers, financial and health crises," Annals of Operations Research, Springer, vol. 313(2), pages 1077-1116, June.
    9. M. Karanasos & S. Yfanti & A. Christopoulos, 2021. "The long memory HEAVY process: modeling and forecasting financial volatility," Annals of Operations Research, Springer, vol. 306(1), pages 111-130, November.
    10. Guglielmo Maria Caporale & Menelaos Karanasos & Stavroula Yfanti, 2019. "Macro-Financial Linkages in the High-Frequency Domain: The Effects of Uncertainty on Realized Volatility," CESifo Working Paper Series 8000, CESifo.
    11. Samir Orujov & Victor Elvira & Audrey Poterie & Farid Rajabov & Francois Septier, 2025. "VS-LTGARCHX: A Flexible Variable Selection in Log-TGARCHX Models," Post-Print hal-04283159, HAL.

    More about this item

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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