Inference for Long-memory Processes Using Local Lyapunov Exponents

Alex  C. Gonzaga,

Inference for Long-memory Processes Using Local Lyapunov Exponents

Discipline: Mathematics, Natural Sciences

Abstract:

Local Lyapunov exponent (LLE) is a finite-time version of Lyapunov exponent, a tool for analyzing chaos. In this paper, we propose a new approach in analyzing long-memory time series. We apply LLE in the context of long-memory processes. The distribution function of the LLE for ARFIMA (p,d,q) process is derived, and an unbiased estimator and some uniformly most powerful tests for long-memory are proposed.