ﻻ يوجد ملخص باللغة العربية
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 $mu (0)$ or the average trend $int_{0}^{1} mu (t) dt$). The problem is motivated by a more realistic modelling of change point analysis, where one is interested in identifying relevant deviations in a smoothly varying sequence of means $ (mu (i/n))_{i =1,ldots ,n }$ and cannot assume that the sequence is piecewise constant. A test for this type of hypotheses is developed using an appropriate estimator for the integrated squared deviation of the mean function and the threshold. By a new concept of self-normalization adapted to non-stationary processes an asymptotically pivotal test for the hypothesis of a relevant deviation is constructed. The results are illustrated by means of a simulation study and a data example.
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
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 o
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,
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
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