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 for the time interval increases with a power law for small time but saturates at sufficiently large time. The exponent changes with the power exponent of the memory kernel.