Anomalous Fluctuations in Autoregressive Models with Long-Term Memory

An autoregressive model with a power-law type memory kernel is studied as a stochastic process that exhibits a self-affine-fractal-like behavior for a small time scale. We find numerically that the root-mean-square displacement Delta(m) for the time interval m increases with a power law as m(alpha) with alpha < 1/2 for small m but saturates at sufficiently large m. The exponent a changes with the power exponent of the memory kernel.