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Noncausal AR processes driven by causal GARCH volatility

Author

Listed:
  • Daniel Velásquez-Gaviria

    (School of Business and Economics, Department of Quantitative Economics, Maastricht, The Netherlands)

  • Jean-Michel Zakoïan

    (CREST-ENSAE, France)

Abstract

This paper studies the introduction of causal conditional heteroskedasticity in noncausal autoregressive (AR) models. We demonstrate that, in this framework, large shocks to the independent innovation that drives the GARCH error term of a noncausal AR(1) model result in heightened volatility following a bubble crash. The non-coincidence of the σ-fields generated by past observations and past values of the GARCH process makes estimation nonstandard. In particular, the full quasi-maximum likelihood estimator (QMLE) is generally inconsistent. We investigate the asymptotic properties of three-step weighted least squares estimators of the AR coefficient and the QMLE of the volatility parameters. Our findings are illustrated via Monte Carlo experiments and real financial data.

Suggested Citation

  • Daniel Velásquez-Gaviria & Jean-Michel Zakoïan, 2026. "Noncausal AR processes driven by causal GARCH volatility," Working Papers 2026-02, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2026-02
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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • 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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