Change point analysis of covariance functions: A weighted cumulative sum approach

We develop and study change point detection estimation procedures for the covariance kernel of functional data based on norms a generally weighted process partial sample estimates. It is shown under mild weak dependence moment conditions that in absence detector integrating such over parameter asymptotically distributed as norm Gaussian process, which furnishes consistent procedure. further derive consistency local asymptotic results this presence function. The corresponding estimator also to be rate optimal estimating an existing point, argument maximum framework. small simulation detect changes autoregressive generalized conditionally heteroscedastic processes, demonstrate use CUSUM statistics context improves performance methods. These new are demonstrated application detecting volatility high resolution intraday asset price curves derived from oil futures prices.