Subsampling tests for the mean change point with heavy-tailed innovations

The quest of the mean change point with innovations in the domain of attraction of a κ-stable law appears to still be ongoing. We adopt the residual CUSUM of squares test (RCUSQ) and derive its null asymptotic distribution, which is dependent on stable index κ. Then a residual-based subsampling is proposed to approximate the null distribution when stable index κ is unknown. Consistency and the rate of convergence for the estimated change point are also obtained. We establish the asymptotic validity of this method and assess its performance both theoretically and numerically.