Conference Agenda

Appropriate preprocessing is a fundamental prerequisite for analyzing a noisy dataset. The aim of this paper is to utilize the nonparametric preprocessing method known as (Multivariate) Singular Spectrum Analysis ((M)SSA) on various (multivariate) datasets. These datasets are then subjected to multiple statistical hypothesis tests. In this study, we compare (M)SSA with three other state-of-the-art preprocessing methods in terms of denoising quality and the statistical power of subsequent multiple tests. The competing methods include both parametric and nonparametric approaches. Furthermore, we investigate the effectiveness of these preprocessing methods in controlling type I errors, which play a critical role in ensuring the reliability of statistical inferences. Our evaluation primarily focuses on the (empirical) Family-Wise Error Rate (FWER) and on empirical power. We utilize these metrics to assess the ability of (M)SSA, particularly, to maintain the desired level of error control and to demonstrate its superiority in terms of empirical power over other methods. This analysis provides valuable insights into the robustness and reliability of the preprocessing methods, particularly in terms of noise reduction, and their ability to control the empirical type I error rate effectively across simulated and real-world datasets. Our findings demonstrate that (M)SSA can be considered a promising method to reduce noise, extract the main signal from noisy data, and detect statistically significant signal components.

For time series data observed at non-random and possibly non-equidistant time points, we estimate the trend function nonparametrically. Under the assumption of bounded total variation of the trend function we propose a nonlinear wavelet estimator which uses a Haar-type basis adapted to a possibly non-dyadic sample size. An appropriate thresholding scheme for sparse signals with an additive polynomial-tailed noise is first derived in an abstract framework and then applied to the problem of trend estimation.

In this talk, we consider peaks-over-threshold (POT) estimators for extremes of long memory linear time series. As these time series are not beta-mixing, classical asymptotic results on POT estimators are not applicable. We adapt a reduction principle for subordinated long memory linear time series to our setting. Thus we prove a central limit theorem for POT estimators, including the Hill estimator. We obtain convergence to stable limit distributions with different rates for light and heavy tails.

We first introduce time-varying Lévy-driven state space models, as a class of time series models in continuous time encompassing continuous-time autoregressive moving average processes with parameters changing over time. In order to allow for their statistical analysis we define a notion of locally stationary approximations for sequences of continuous time processes and establish laws of large numbers and central limit type results under θ-weak dependence assumptions. Finally, we consider the asymptotic behaviour of the empirical mean and autocovariance function of time-varying Lévy-driven state space models under appropriate conditions.