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Aggregationn of Space-Time Processes


  • Giacomini, Raffaella
  • Granger, Clive W.J.


In this paper we compare the relative efficiency of different methods of forecasting the aggregate of spatially correlated variables. Small sample simulations confirm the asymptotic result that improved forecasting performance can be obtained by imposing a priori constraints on the amount of spatial correlation in the system. One way to do so is to aggregate forecasts from a Space-Time Autoregressive model (Cliff et al., 1975), which offers a solution to the 'curse of dimensionality' that arises when forecasting with VARs. We also show that ignoring spatial correlation, even when it is weak, leads to highly inaccurate forecasts. Finally, if the system satisfies a 'poolability' condition, there is a benefit in forecasting the aggregate variable directly.

Suggested Citation

  • Giacomini, Raffaella & Granger, Clive W.J., 2001. "Aggregationn of Space-Time Processes," University of California at San Diego, Economics Working Paper Series qt77f76455, Department of Economics, UC San Diego.
  • Handle: RePEc:cdl:ucsdec:qt77f76455

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    References listed on IDEAS

    1. Granger, C. W. J., 1987. "Implications of Aggregation with Common Factors," Econometric Theory, Cambridge University Press, vol. 3(02), pages 208-222, April.
    2. Kohn, Robert, 1982. "When is an aggregate of a time series efficiently forecast by its past?," Journal of Econometrics, Elsevier, vol. 18(3), pages 337-349, April.
    3. F Stetzer, 1982. "Specifying weights in spatial forecasting models: the results of some experiments," Environment and Planning A, Pion Ltd, London, vol. 14(5), pages 571-584, May.
    4. Pinkse, Joris & Slade, Margaret E., 1998. "Contracting in space: An application of spatial statistics to discrete-choice models," Journal of Econometrics, Elsevier, vol. 85(1), pages 125-154, July.
    5. Aigner, Dennis J & Goldfeld, Stephen M, 1974. "Estimation and Prediction from Aggregate Data when Aggregates are Measured More Accurately than Their Components," Econometrica, Econometric Society, vol. 42(1), pages 113-134, January.
    6. Brown, Bryan W. & Mariano, Roberto S., 1989. "Predictors in Dynamic Nonlinear Models: Large-Sample Behavior," Econometric Theory, Cambridge University Press, vol. 5(03), pages 430-452, December.
    7. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
    8. Patrick E. Brown & Gareth O. Roberts & Kjetil F. Kåresen & Stefano Tonellato, 2000. "Blur-generated non-separable space-time models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 847-860.
    9. Tobias, Justin & Zellner, Arnold, 2000. "A Note on Aggregation, Disaggregation and Forecasting Performance," Staff General Research Papers Archive 12024, Iowa State University, Department of Economics.
    10. F Stetzer, 1982. "Specifying Weights in Spatial Forecasting Models: The Results of Some Experiments," Environment and Planning A, , vol. 14(5), pages 571-584, May.
    11. Thomas Doan & Robert B. Litterman & Christopher A. Sims, 1983. "Forecasting and Conditional Projection Using Realistic Prior Distributions," NBER Working Papers 1202, National Bureau of Economic Research, Inc.
    12. Baillie, Richard T., 1980. "Predictions from ARMAX models," Journal of Econometrics, Elsevier, vol. 12(3), pages 365-374, April.
    13. Pesaran, M Hashem & Pierse, Richard G & Kumar, Mohan S, 1989. "Econometric Analysis of Aggregation in the Context of Linear Prediction Models," Econometrica, Econometric Society, vol. 57(4), pages 861-888, July.
    14. Bronars, Stephen G. & Jansen, Dennis W., 1987. "The geographic distribution of unemployment rates in the U.S. : A spatial-time series analysis," Journal of Econometrics, Elsevier, vol. 36(3), pages 251-279, November.
    15. Hirotugu Akaike, 1969. "Fitting autoregressive models for prediction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 243-247, December.
    16. Hall, Alastair R, 1994. "Testing for a Unit Root in Time Series with Pretest Data-Based Model Selection," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 461-470, October.
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    More about this item


    spatial correlation; aggregation; forecast efficiency; space-time models;

    JEL classification:

    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods


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