Coverage bound for fixed-b subsampling and generalized subsampling for time series

We investigate the upper bounds on coverage probabilities of the subsampling-based confidence sets in the time series setting. Under the fixed-b asymptotic framework, where b is the ratio of block size to sample size, we derive the limiting coverage bound, and obtain the finite sample coverage bound by simulations. Our findings suggest that the coverage bound is strictly below 1 for positive b, it can be far away from 1, and the fixed-b subsampling method in Shao and Politis (2013) can exhibit serious undercoverage when the dimension of the parameter is large, the time series dependence is (positively) strong, or b is large. To alleviate the problem, we propose a generalized subsampling method that combines useful features of fixed-b subsampling and self-normalization, and demonstrate its effectiveness in terms of delivering more accurate coverage via numerical studies.