Keywords: change detection, functional time series, temporal-dependence
Abstract
We consider functional autoregressive time series observed sparsely with noise. Using robust Kalman filtering and efficient blocked Gibbs sampling, we fit a state-space model. The interest is in detection of change point in any of the three parameters, the mean, the variance and the autocovariance operator. We extend the method to detect simultaneous shifts across multiple parameters. Identifying the posterior mode as the change point, we obtain very promising results in simulations under several situations. We apply the method to obtain change points in high frequency financial data as well as temperature data.
