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This paper aims at providing statistical guarantees for a kernel based estimation of time varying parameters driving the dynamic of local stationary processes. We extend the results of Dahlhaus et al. (2018) considering the local stationary version of the infinite memory processes of Doukhan and Wintenberger (2008). The estimators are computed as localized M-estimators of any contrast satisfying appropriate contraction conditions. We prove the uniform consistency and pointwise asymptotic normality of such kernel based estimators. We apply our result to usual contrasts such as least-square, least absolute value, or quasi-maximum likelihood contrasts. Various local-stationary processes as ARMA, AR(infty), GARCH, ARCH(infty), ARMA-GARCH, LARCH(infty),..., and integer valued processes are also considered. Numerical experiments demonstrate the efficiency of the estimators on both simulated and real data sets.
In this paper we consider multivariate Hawkes processes with baseline hazard and kernel functions that depend on time. This defines a class of locally stationary processes. We discuss estimation of the time-dependent baseline hazard and kernel functi
Locally stationary Hawkes processes have been introduced in order to generalise classical Hawkes processes away from stationarity by allowing for a time-varying second-order structure. This class of self-exciting point processes has recently attracte
In this contribution we introduce weakly locally stationary time series through the local approximation of the non-stationary covariance structure by a stationary one. This allows us to define autoregression coefficients in a non-stationary context,
In the common time series model $X_{i,n} = mu (i/n) + varepsilon_{i,n}$ with non-stationary errors we consider the problem of detecting a significant deviation of the mean function $mu$ from a benchmark $g (mu )$ (such as the initial value $mu (0)$ o
The problem of constructing a simultaneous confidence band for the mean function of a locally stationary functional time series $ { X_{i,n} (t) }_{i = 1, ldots, n}$ is challenging as these bands can not be built on classical limit theory. On the one