In this paper, we investigate the problem of detecting a change-point in a multiple time-series for both fixed and high-dimensions. For the fixed dimensional case, we detect change-points for each individual co-ordinates using a moving average technique and focus on testing synchronization of these change-points. The identification of synchronized change-points can often lead to finding an unanimous reason behind such changes. We provide an application of our study in speedy recovery of power grid system. Testing for Synchronization in High Dimension is also discussed.

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.

We consider maximum deviations of sample autocovariances and autocorrelations from their theoretical counterparts over a number of lags that increases with the number of observations. The asymptotic distribution of such statistics e.g. for strictly stationary time series is of Gumbel type. However speed of convergence to the Gumbel distribution is rather slow. The well-known autoregressive (AR) sieve bootstrap is asymptotically valid for such maximum deviations but suffers from the same slow convergence rate. Braumann et al. 2021 showed that for linear time series the AR sieve bootstrap speed of convergence is of polynomial order. We use the idea of Gaussian approximation for high-dimensional time series to show that for the class of strictly stationary processes a wild-type bootstrap and a hybrid variant of the AR sieve bootstrap are asymptotically valid for our statistic of interest at a polynomial convergence rate. We close with results from a small simulation study that investigates finite sample properties of mentioned bootstrap proposals.