Population Forecasting in a Modern Metropolis (using St. Petersburg as a Case Study): Methodological Aspects

Abstract

This article examines probabilistic cohort-component forecasting of the population of a megacity as an open demographic system, where migration determines the dynamics of the po­pulation size and age structure. In the methodology under consideration, fertility, mortality, and migration are modeled as stochastic age-sex processes: age profiles are reduced using PCA, the dynamics of time coefficients are described by AR(1) (equivalent ARIMA (1,0,0)), and the forecast is generated as a distribution of trajectories in a Monte Carlo simulation. The migration component is specified through relative age-sex rates with drift and an additional level adjustment (bump component) reflecting the possible underestimation of migration growth; interval estimates are validated by backtesting and calibrated against empirical coverage. All calculations are based on St. Petersburg data; the empirical base covers 1990–2023, and the forecast horizon extends to 2045, ensuring comparability with official Rosstat estimates. The median trajectory marks the city's transition to a demographic plateau: by 2045, the population will reach 5.62 million, with a 90% range of 5.225–6.041 million. Simultaneously, population aging accelerates (the share of residents aged 65+ reaches 23% by 2045), and the role of migration shifts from a source of growth to a mechanism for compensating for natural decline and stabilizing the age structure. Scenario forecasts show that the long-term fork in the trajectory is determined primarily by the cumulative migration effect (by 2045, from 5.32 million to 6.40 million in extreme cases). A comparison with the Rosstat forecast reveals moderate discrepancies; the official forecast trajectory falls within the confidence intervals of the probability model. The proposed toolkit can be used for population forecasting at the level of major cities and regions across the country.