Noncausal AR processes driven by causal GARCH volatility

Daniel Velásquez-Gaviria () and Jean-Michel Zakoïan
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Daniel Velásquez-Gaviria: School of Business and Economics, Department of Quantitative Economics, Maastricht, The Netherlands
Jean-Michel Zakoïan: CREST-ENSAE, France

No 2026-02, Working Papers from Center for Research in Economics and Statistics

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.

Keywords: Bubbles; Conditional Heteroskedasticity; Noncausal Autoregression; Quasi-Maximum Likelihood Estimation; Weighted Least Squares (search for similar items in EconPapers)
JEL-codes: C13 C22 C58 (search for similar items in EconPapers)
Pages: 52 pages
Date: 2026-01-15
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