Varieties of long memory models

Long memory is defined as a series having a slowly declining correlogram or, equivalently, an infinite spectrum at zero frequency. Fractional integrated processes have such properties but here it is pointed out that a number of other processes can also be long memory, including generalized fractionally integrated models arising from aggregation, time-changing coefficient models, and possibly nonlinear models. It seems that there are many classes of processes that deserve further study. The relevance of long memory is illustrated using absolute returns from a daily stock market index.