Analyzing multivariate time series data is important to predict future events and changes of complex systems in finance, manufacturing, and administrative decisions. The expressiveness power of Gaussian Process (GP) regression methods has been significantly improved by compositional covariance structures. In this paper, we present a new GP model which naturally handles multiple time series by placing an Indian Buffet Process (IBP) prior on the presence of shared kernels. Our selective covariance structure decomposition allows exploiting shared parameters over a set of multiple, selected time series. We also investigate the well-definedness of the models when infinite latent components are introduced. We present a pragmatic search algorithm which explores a larger structure space efficiently. Experiments conducted on five real-world data sets demonstrate that our new model outperforms existing methods in term of structure discoveries and predictive performances.