Contrast estimation of time-varying infinite memory processes

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.