A tail index estimation for long memory processes

This paper provides a least squares regression estimation of the tail index for long memory processes where the innovations are \(\alpha \)-stable random sequences. The estimate is based on the property of the characteristic function of the process near the origin. The asymptotics of the estimator are obtained by choosing suitable regression samples with the help of the properties of the \(\alpha \)-stable distribution. The numerical simulation and an empirical analysis of financial market data are conducted to assess the finite sample performance of the proposed estimator.