Many researchers have used time series models to construct population forecasts and prediction intervals at the national level, but few have evaluated the accuracy of their forecasts or the out-of-sample validity of their prediction intervals. Fewer still have developed models for subnational areas. In this study, we develop and evaluate six ARIMA time series models for states in the United States. Using annual population estimates from 1900 to 2000 and a variety of launch years, base periods, and forecast horizons, we construct population forecasts for four states chosen to reflect a range of population size and growth rate characteristics. We compare these forecasts with population counts for the corresponding years and find precision, bias, and the width of prediction intervals to vary by state, launch year, model specification, base period, and forecast horizon. Furthermore, we find that prediction intervals based on some ARIMA models provide relatively accurate forecasts of the distribution of future population counts but prediction intervals based on other models do not. We conclude that there is some basis for optimism regarding the possibility that ARIMA models might be able to produce realistic prediction intervals to accompany population forecasts, but a great deal of work remains to be done before we can draw any firm conclusions.
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Ahlburg, D. (1992). Error measures and the choice of a forecast method. International Journal of Forecasting, 8, 99–100.
Alho, J. (1990). Stochastic methods in population forecasting. International Journal of Forecasting, 6, 521–530.
Alho, J., & Spencer, B. (1997). The practical specification of the expected error of population forecasts. Journal of Official Statistics, 13, 203–225.
Box, G., & Jenkins, G. (1976). Time series analysis: Forecasting and control. San Francisco, CA: Holden Day.
Brockwell, P., & Davis, R. (2002). Introduction to time series and forecasting (2nd ed.). New York, NY: Springer-Verlag.
Chatfield, C. (2000). Time-series forecasting. Boca Raton, FL: Chapman & Hall/CRC.
Cohen, J. (1986). Population forecasts and confidence intervals for Sweden: A comparison of model-based and empirical approaches. Demography, 23, 105–126.
De Beer, J. (1993). Forecast intervals of net migration: The case of the Netherlands. Journal of Forecasting, 12, 585–599.
Dickey, D., Bell, W., & Miller, R. (1986). Unit roots in time series models: Tests and implications. American Statistician, 74, 427–431.
Granger, C. (1989). Forecasting in business and economics (2nd ed.). San Diego, CA: Academic Press.
Granger, C., & Newbold, P. (1986). Forecasting economic time series (2nd ed.). San Diego, CA: Academic Press.
Keilman, N. (1999). How accurate are the United Nations world population projections? In W. Lutz, J. Vaupel, & D. Ahlburg (Eds.), Frontiers of population forecasting (pp. 15–41). New York, NY: Population Council. Supplement to Vol. 24 of Population and Development Review.
Keilman, N., Pham, D., & Hetland, A. (2002). Why population forecasts should be probabilistic – illustrated by the case of Norway. Demographic Research, 6, 409–453.
Keyfitz, N. (1977). Applied mathematical demography. New York, NY: John Wiley.
Keyfitz, N. (1981). The limits of population forecasting. Population and development review, 7, 579–593.
Lee, R. (1974). Forecasting births in post-transition populations: Stochastic renewal with serially correlated fertility. Journal of the American Statistical Association, 69, 607–617.
Lee, R. (1992). Stochastic demographic forecasting. International Journal of Forecasting, 8, 315–327.
Lee, R., & Tuljapurkar, S. (1994). Stochastic population forecasts for the United States: Beyond high, medium, and low. Journal of the American Statistical Association, 89, 1175–1189.
Lutz, W., Sanderson, W., & Scherbov, S. (1999). Expert-based probabilistic population projections. In W. Lutz, J. Vaupel, & D. Ahlburg (Eds.), Frontiers of Population Forecasting (pp. 139–155). New York, NY: Population Council. Supplement to Vol. 24 of Population and Development Review.
Makridakis, S., Wheelwright, S., & Hyndman, R. (1998). Forecasting methods and applications (3rd ed.). New York, NY: John Wiley.
McCleary, R., & Hay, R. (1980). Applied time series for the social sciences. Beverly Hills, CA: Sage Publications.
McNown, R., & Rogers, A. (1989). Forecasting mortality: A parameterized time series approach. Demography, 26, 645–660.
Meyler, A., Kenny, G., & Quinn, T. (1998). Forecasting Irish inflation using ARIMA models. Technical Paper 3/RT/98. Economic Analysis, Research, and Publication Department. Central Bank of Ireland.
Murdock, S., Leistritz, F., Hamm, R., Hwang, S., & Parpia, B. (1984). An assessment of the accuracy of a regional economic-demographic projection model. Demography, 21, 383–404.
Nelson, C. (1973). Applied time series analysis for managerial forecasting. San Francisco, CA: Holden Day.
Pflaumer, P. (1992). Forecasting U.S. population totals with the Box–Jenkins approach. International Journal of Forecasting, 8, 329–338.
Rayer, S. (2004). Assessing the accuracy and bias of trend extrapolation methods for population projections: The long view. Paper presented at the annual meeting of the Southern Demographic Association, Hilton Head SC.
Saboia, J. (1974). Modeling and forecasting populations by time series: The Swedish case. Demography, 11, 483–492.
Sanderson, W. (1995). Predictability, complexity, and catastrophe in a collapsible model of population, development, and environmental interactions. Mathematical Population Studies, 5, 259–279.
Smith, S., & Sincich, T. (1988). Stability over time in the distribution of population forecast errors. Demography, 25, 461–474.
Smith, S., & Sincich, T. (1990). The relationship between the length of the base period and population forecast errors. Journal of the American Statistical Association, 85, 367–375.
Smith, S., & Sincich, T. (1992). Evaluating the forecast accuracy and bias of alternative population projections for states. International Journal of Forecasting, 8, 495–508.
Smith, S., Tayman, J., & Swanson, D. (2001). State and local population projections: Methodology and analysis. New York, NY: Kluwer Academic/Plenum Publishers.
Stoto, M. (1983). The accuracy of population projections. Journal of the American Statistical Association, 78, 13–20.
Swanson, D., & Beck, D. (1994). A new short-term county population projection method. Journal of Economic and Social Measurement, 20, 25–50.
Tayman, J. (1996). The accuracy of small-area population forecasts based on a spatial interaction land-use modeling system. Journal of the American Planning Association, 62, 85–98.
Tayman, J., Rayer, S., & Smith, S. (2005). Prediction intervals for county population forecasts. Paper presented at the annual meeting of the Southern Demographic Association, Oxford MS.
Tayman, J., Schafer, E., & Carter, L. (1998). The role of population size in the determination and prediction of population forecast errors: An evaluation using confidence intervals for subcounty areas. Population Research and Policy Review, 17, 1–20.
U.S. Census Bureau. (1956). Estimates of the population of states: 1900 to 1949. Current Population Reports, Series P-25, No. 139 (Released on the Internet February 1996.)
U.S. Census Bureau. (1965). Revised estimates of the population of states and components of population change 1950 to 1960. Current Population Reports, Series P-25, No. 304 (Released on the Internet April 1995.)
U.S. Census Bureau. (1971). Preliminary intercensal estimates of states and components of population change 1960 to 1970. Current Population Reports, Series P-25, No. 460 (Released on the Internet August 1996.)
U.S. Census Bureau. (1984). Intercensal estimates of states and components of population change 1970 to 1980. Current Population Reports, Series P-25, No. 957 (Released on the Internet February 1995.)
U.S. Census Bureau. (1993). Intercensal estimates of states and components of population change 1970 to 1980. Current Population Reports, Series P-25, No. 1106 (Released on the Internet August 1996.)
U.S. Census Bureau. (2002). Table CO-EST2001-12-0 – Series of intercensal state population estimates: April 1, 1990 to April 1, 2000. (Released on the Internet April 2002.)
Voss, P., Palit, C., Kale, B., & Krebs, H. (1981). Forecasting state populations using ARIMA time series techniques. Report prepared by the Wisconsin Department of Administration and the University of Wisconsin-Madison.
White, H. (1954). Empirical study of the accuracy of selected methods of projecting state populations. Journal of the American Statistical Association, 49, 480–498.
The authors thank the two referees for their thoughtful comments and suggestions that greatly improved this paper.
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Tayman, J., Smith, S.K. & Lin, J. Precision, bias, and uncertainty for state population forecasts: an exploratory analysis of time series models. Popul Res Policy Rev 26, 347 (2007). https://doi.org/10.1007/s11113-007-9034-9
- Forecast accuracy
- Forecast uncertainty
- Population forecasts
- Prediction intervals