If there is long-term memory in property stocks and REITs prices, historical data is relevant for future prices prediction. Despite previous research adopted various different methods to forecast future asset prices by using historical data; we attempted to forecast the REITs and stock indices by Group Method of Data Handling (GMDH) neural network method with Hurst which is the first of its kind. Our results showed that GMDH neural network performed better than the classical forecasting algorithms such as Single Exponential Smooth, Double Exponential Smooth, ARIMA and back-propagation neural network. The research results also provide useful information for investors when they make investment decisions.