10 papers
A Functional Central Limit Theorem for Locally Stationary Time Series in Banach Spaces
Florian Heinrichs, Luis-Alberto Rodríguez
A functional central limit theorem for locally stationary time series taking values in a separable Banach space is established. The result does not require type-2 or cotype ass…
Testing for Stable Intervals in Non-Stationary Time Series
Florian Heinrichs
Many time series are not stable over their full observation horizon, but may contain scientifically meaningful periods during which a signal remains stable up to a prescribed toler…
A Functional Central Limit Theorem for Localized Partial Sums of Non-Stationary Time Series
Florian Heinrichs
A localized functional central limit theorem is established for kernel-weighted partial sum processes of piecewise locally stationary time series under geometric decay of the physi…
Self-Normalization for CUSUM-based Change Detection in Locally Stationary Time Series
Florian Heinrichs
A new bivariate partial sum process for locally stationary time series is introduced and its weak convergence to a Brownian sheet is established. This construction enables the deve…
Sequential Outlier Detection in Non-Stationary Time Series
Florian Heinrichs, Patrick Bastian, Holger Dette
A novel method for sequential outlier detection in non-stationary time series is proposed. The method tests the null hypothesis of ``no outlier'' at each time point, addressing the…
Functional Neural Networks: Shift invariant models for functional data with applications to EEG classification
Florian Heinrichs, Mavin Heim, Corinna Weber
It is desirable for statistical models to detect signals of interest independently of their position. If the data is generated by some smooth process, this additional structure sho…
A Portmanteau-type test for detecting serial correlation in locally stationary functional time series
Axel Bücher, Holger Dette, Florian Heinrichs
The Portmanteau test provides the vanilla method for detecting serial correlations in classical univariate time series analysis. The method is extended to the case of observations…
A distribution free test for changes in the trend function of locally stationary processes
Holger Dette, Florian Heinrichs
In the common time series model with non-stationary errors we consider the problem of detecting a significant deviation of the mean function…
Are deviations in a gradually varying mean relevant? A testing approach based on sup-norm estimators
Axel Bücher, Holger Dette, Florian Heinrichs
Classical change point analysis aims at (1) detecting abrupt changes in the mean of a possibly non-stationary time series and at (2) identifying regions where the mean exhibits a p…
Detecting deviations from second-order stationarity in locally stationary functional time series
Axel Bücher, Holger Dette, Florian Heinrichs
A time-domain test for the assumption of second order stationarity of a functional time series is proposed. The test is based on combining individual cumulative sum tests which are…