Conference Agenda

Injuries to the lower extremity joints are often debilitating, particularly for professional athletes. Understanding the onset of stressful conditions on these joints is therefore important in order to ensure prevention of injuries as well as individualised training for enhanced athletic performance. We study the biomechanical joint angles from the hip, knee and ankle for runners who are experiencing fatigue. The data is cyclic in nature and densely collected by body worn sensors, which makes it ideal to work with in the functional data analysis (FDA) framework.

We develop a new method for multiple change point detection for functional data, which improves the state of the art with respect to at least two novel aspects. First, the curves are compared with respect to their maximum absolute deviation, which leads to a better interpretation of local changes in the functional data compared to classical $L^2$-approaches. Secondly, as slight aberrations are to be often expected in a human movement data, our method will not detect arbitrarily small changes but hunts for relevant changes, where maximum absolute deviation between the curves exceeds a specified threshold, say $\Delta >0$. We recover multiple changes in a long functional time series of biomechanical knee angle data, which are larger than the desired threshold $\Delta$, allowing us to identify changes purely due to fatigue. In this work, we analyse data from both controlled indoor as well as from an uncontrolled outdoor (marathon) setting.

Some recent results on functional linear models with scalar response and functional covariate are presented. In those models it is more challenging to deal with residual-based procedures than in regression models with vector-valued covariates. We present procedures for testing for changes in the error distribution, goodness-of-fit testing, and testing for independence of covariates and errors. We also consider models with vector-valued responses and functional covariates. Here the dependence between the components of the response, given the covariate, can be modeled by the copula of vector-valued errors, and we present the asymptotics of the residual-based empirical copula.

Multivariate locally stationary functional time series provide a flexible framework for modeling complex data structures exhibiting both temporal and spatial dependencies while allowing for time-varying data generating mechanism. In this study, we introduce a specialized Portmanteau test tailored for assessing white noise assumptions for multivariate locally stationary functional time series without dimension reduction. Our approach is based on a new Gaussian approximation result for the kernel-weighted second-order functional time series, which is of independent interest. A simple bootstrap procedure is proposed to implement the test because the limiting distribution can be non-standard or even does not exist. Through theoretical analysis and simulation studies, we demonstrate the efficacy and adaptability of the proposed portmanteau test in detecting departures from white noise assumptions in multivariate locally stationary functional time series.

In the functional data setting, we study a new goodness-of-fit test for the composite null hypothesis that the data are coming from a geometric Brownian motion, or equivalent from a scaled Brownian motion with linear drift. Critical values are easily obtained and ensure that the test keeps the significance level in the finite sample case. New theoretical results investigate limits of the test statistic as the sample size tends to infinity, under the null hypothesis and under alternatives, and show the consistency of the test. Another advantage of the new approach is a fast and simple implementation and finally the reduction of computational effort. Moreover, in a comprehensive simulation study, the novel test compares favourably against competitors. An obvious application is for testing financial time series whether the Black-Scholes model applies. For illustration, we provide data examples for different stock and interest rate time series.