Real estate market price forecasting is always in the focus of interests of scientists-economists, market analysts, market participants (sellers and buyers), marketing services of building complex enterprises, analysts working for banks and insurance companies and investors. Under present day conditions, the price behavior of properties on real estate markets takes especially important meaning subject to the influence of such factors as changes in the structure of household incomes, changes in mortgage rates and their availability, dynamic changes in the macroeconomic and other external socio-economic and political type factors. However, unlike the financial and securities markets, the real estate market is always characterized by a delayed reaction to external perturbations, often up to half a year, which allows us to hope for an appropriate construction of forecasts, at least in time for the delayed reaction. Traditional autoregressive forecasting methods are characterized by rapidly increasing forecast variance, because they assume a factor of stochastic volatility. This paper proposes a model and method of forecast construction based on stochastic processes of the “Poisson random index” having a short time for reaching a stationary stable variance. The model is based on the “principle of replacements” of current prices with new ones. We analyze in detail an example of the application of the “principle of replacements” for construction of price forecasts on secondary residential real estate in St. Petersburg which is based on data of four-year observations of offer prices.