Abstract
This paper calculates the memory of fractionally integrated ARMA(1,d, 1) processes. It is shown that fractional integration can enhance the memory of common ARMA processes enormously, but also that this is not necessarily the case. Very long memory is found for positively fractionally integrated processes with large positive autoregressive parameters. On the contrary, large negative AR parameters absorb the memory generated by a positive differencing parameter to a great extent. A moving average parameter may also reduce the memory substantially, even if the parameter alone causes virtually no memory.