Abstract
We consider robust estimation of the tail index a for linear long-memory processes with i.i.d. innovations ej following a symmetric a-stable law (1 < a < 2) and coefficients aj similar to c.j-beta. Estimates based on the left and right tail respectively are obtained together with a combined statistic with improved efficiency, and a test statistic comparing both tails. Asymptotic results are derived. Simulations illustrate the finite sample performance.