Contrast estimation of time-varying infinite memory processes

Jean-Marc Bardet, Paul Doukhan and Olivier Wintenberger

Stochastic Processes and their Applications, 2022, vol. 152, issue C, 32-85

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.

Date: 2022
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DOI: 10.1016/j.spa.2022.06.005

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