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Contrast estimation of time-varying infinite memory processes

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  • Bardet, Jean-Marc
  • Doukhan, Paul
  • Wintenberger, Olivier

Abstract

This paper extends the study of kernel-based estimation for locally stationary processes proposed in Dahlhaus et al., 2019 to infinite-memory processes models such as locally stationary AR(∞), GARCH(p,q), ARCH(∞) or LARCH(∞) processes. The estimators are computed as localized M-estimators for every contrast satisfying appropriate regularity conditions. We prove the uniform consistency and pointwise asymptotic normality of such kernel-based estimators. We apply our results to common contrasts such as least-square, least-absolute-value, or quasi-maximum likelihood contrast. Numerical experiments demonstrate the efficiency of the estimators on both simulated and real data sets.

Suggested Citation

  • Bardet, Jean-Marc & Doukhan, Paul & Wintenberger, Olivier, 2022. "Contrast estimation of time-varying infinite memory processes," Stochastic Processes and their Applications, Elsevier, vol. 152(C), pages 32-85.
    • Handle: RePEc:eee:spapps:v:152:y:2022:i:c:p:32-85
    DOI: 10.1016/j.spa.2022.06.005
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    References listed on IDEAS

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