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Kopnova E. D., Rodionova L. A. The Statistical Approach to the Analysis and Forecasting of Demographic Data. Izv. Saratov Univ. (N. S.), Ser. Economics. Management. Law, 2016, vol. 16, iss. 3, pp. 306-? DOI:


The Statistical Approach to the Analysis and Forecasting of Demographic Data

Introduction. Possibilities of application ARIMA-models to analysis and forecasting of demographic time series were considered in the article. Foreign studies had shown that the ARIMA-models give good results for forecasting indicators such as population, birth rates and death rates, life expectancy, along with the traditional demographic methods (cohort-component approach). Research technique. Box – Jenkins methodology of the analysis and forecasting of time series, particularly with regard to demographic data: total fertility rate in Russia (1990–2014), the number of marriages by months in Russia (2005–2015), total fertility rate in France (1740–2014) and the unemployment rate in Russia (1996–2016) was used in the work. ARIMA-, ARIMA- and ARIMA-models, depending on the nature of the dynamics of the studied indicators were analyzed. Results. The analysis had shown that the estimated ARIMA-models for the total fertility rate and number of marriages were adequate and had good statistical and prognostic properties. Forecasts were built on basis of the obtained models. In the case of long series availability of properties with a long memory processes have not been identified.


1. Box G. P., Jenkins G. M. Time Series Analysis Forecasting and Control. San Francisco: Holden-Day, 1970. 554 p.
2. Hiorns R. W. Mathematical Models in Demography. The Structure of Human Populations. Ed. by G. A. Harrison, A. Z. Boycl. Oxford, Clarendon Press, 1972, pp. 110–127.
3. Lee R. Forecasting Births in Post-Transition Populations. Journal of the American Statistical Association, 1974, vol. 69, pp. 607–617.
4. Pollard J. H. On Simple Approximate Calculations Appropriate to Populations with Random Growth Rates. Theoretical Population Biology, 1970, vol. 1, pp. 208–218. 5. Saboia J. L. M. Modeling and Forecasting Populations by Time Series ‒ The Swedish Case. Demography, 1974, vol. 11, pp. 483–492.
6. Kashyap R. L., Rao A. R. Dynamic Stochastic Models from Empirical Data. New York, London, Academic Press, 1976. 352 p.
7. Saboia J. L. M. Autoregressive Integrated Moving Average (ARIMA) Models for Birth Forecasting. Journal of the American Statistical Association, 1977, vol. 72 (358), pp. 264–270.
8. Pfl aumer Р. Forecasting US population totals with the Box – Jenkins approach. International Journal of Forecasting, 1992, vol. 8, pp. 329–338.
9. Tiziana T., Vaupel J.W. Forecasting life expectancy in an international context. International Journal of Forecasting, 2012, vol. 28, pp. 519–531.
10. Alho J. M., Spencer B. D. Statistical demography and forecasting. Springer, 2005. 410 p.
11. Booth H. Demographic forecasting: 1980 to 2005 in review. International Journal of Forecasting, 2006, vol. 22, pp. 547–581.
12. Rosstat. Available at: (accessed 22 Mart 2016).
13. Mhitarjan V. S., Arhipova M. Ju., Balash V. A., Balash O. S., Dubrova T. A., Sirotin V. P. Ekonometrika [Econometrics. Ed. by V. S. Mhitarjan]. Moscow, Prospekt Publ., 2014. 384 p.
14. Ajvazjan S. A. Metody jekonometriki [Econometrics Methods]. Moscow, INFRA-M Publ., 2010. 510 p.
15. Scherbakova E. Chislo zaregistrirovannykh brakov i razvodov v 2012 godu snizilos’ (The number of registered marriages and divorces decreased in 2012). Demoskop weekly (Demoscope weekly), 2013, № 541–542. Available at: (accessed 20 December 2015).
16. Hurst H. E. Long term Storage Capacity of Reservoirs. Transactions of the American Society of Civil Engineers, 1951, vol. 116, pp. 770–799.
17. Mandelbrot B. Statistical methodology for non-periodic cycles: From the covariance to R/S analysis. Annals of Economic and Social Measurement, 1972, vol. 1, pp. 259–290.
18. Lo A. W. Long-term memory in stock market prices. Econometrica, 1991, vol. 59, pp. 1279–1313.
19. Hyndman R. J., Booth H., Yasmeen F. Coherent Mortality Forecasting: The Product-Ratio Method With Functional Time Series Models. Demography, 2013, vol. 50, iss. 1, pp. 261–283.
20. Granger C. W. Long memory relationships and the aggregation of dynamic models. Journal of Econometrics, 1980, vol. 14, iss. 2, pp. 227–238.
21. Demoskop. Site. Available at: (accessed 22 Mart 2016). 22. World Bank. Site. Available at: (accessed 22 Mart 2016).

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