joint work with Rupsa Basu
Abstract: We present methodology to detect structural breaks in the slope and intercept within the framework of concurrent linear regression for dependent functional time series data in C[0,1]. This is particularly well-suited for multiple functional time series that are collected in parallel or \textit{concurrently}. This enables us to operate within a fully functional framework and analyze how the relationship between the regressor time series and the dependent time series evolves over time. This is done via a CUSUM test statistic composed of Ordinary Least Squares (OLS) residuals and detects breaks in the intercept. To improve the power of detection of breaks in the slope function we propose a modified version of the test statistic for functional data setting, adapted from previous results of Jiang and Kurozumi (2019). Our main theorem for distribution of both test statistics under the null uses an invariance principle for banach space valued random variables given in Dehling (1983). Under the alternative we show the large sample behavior based on deviation in either the slope or intercept. Simulations are provided for IID and AR(1) processes. We show the use of our methods in biomechanical sports data obtained via body-word sensors. We use hip and knee joint angle data from running athletes collected under fatiguing conditions and modeled as dependent variable and the regressor respectively. Athletes experiencing fatigue often exhibit changes in their lower extremity joint angle patterns. Our focus is on detecting changes in the co-movement between two joint angle time series, which can be effectively analyzed as structural breaks in the slope and intercept functions. In this way, we illustrate a practical application of our methods in the biomechanical sciences, enabling practitioners to analyze such data in a meaningful and interpretable manner.
Working paper coming soon