We examine the long memory of real estate investment trust (REIT) volatility in the mature REIT markets of Australia, Japan, the UK and the US, and propose a modified fractionally integrated (FIGARCH) model for forecasting at daily and weekly frequencies. Long memory of volatility occurs when the effects of volatility shocks persist over extended periods of time. Our results suggest that the appearance of long memory in REIT return series is due to a lack of adjustment for temporal changes in the unconditional mean of volatility. Based on our long memory results, we empirically test a modified FIGARCH model and show that it performs better at weekly and daily forecast horizons. Forecasting REIT series volatility has important implications for risk evaluation, portfolio optimisation and derivatives pricing.