Bootstrap Test for Stationarity of Heavy-Tailed Series with Structural Breaks

Abstract:

      The paper proposes a statistic to test stationarity of series with $\kappa$-stable innovations and structural breaks, obtains the asymptotical distribution of the statistic, and proves the consistency of the test. To obtain critic values for the test without the estimation of the index $\kappa$, the paper proposes the bootstrap procedures to approximate the distribution, and proves the consistency of the procedures. The simulations demonstrate that the bootstrap test is practical and powerful.