IDEAS home Printed from https://ideas.repec.org/a/oec/stdkab/5km399r2jz9n.html
   My bibliography  Save this article

Forecasting Aggregated Time Series Variables: A Survey

Author

Listed:
  • Helmut Lütkepohl

Abstract

Aggregated times series variables can be forecasted in different ways. For example, they may be forecasted on the basis of the aggregate series or forecasts of disaggregated variables may be obtained fi rst and then these forecasts may be aggregated. A number of forecasts are presented and compared. Classical theoretical results on the relative effi ciencies of different forecasts are reviewed and some complications are discussed which invalidate the theoretical results. Contemporaneous as well as temporal aggregation are considered. JEL classifi cation : C22, C32 Key Words : Autoregressive moving-average process, contemporaneous aggregation, temporal aggregation, vector autoregressive moving-average process

Suggested Citation

  • Helmut Lütkepohl, 2010. "Forecasting Aggregated Time Series Variables: A Survey," OECD Journal: Journal of Business Cycle Measurement and Analysis, OECD Publishing, Centre for International Research on Economic Tendency Surveys, vol. 2010(2), pages 1-26.
  • Handle: RePEc:oec:stdkab:5km399r2jz9n
    DOI: 10.1787/jbcma-2010-5km399r2jz9n
    as

    Download full text from publisher

    File URL: https://doi.org/10.1787/jbcma-2010-5km399r2jz9n
    Download Restriction: Full text available to READ online. PDF download available to OECD iLibrary subscribers.

    File URL: https://libkey.io/10.1787/jbcma-2010-5km399r2jz9n?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Tae‐Hwan Kim & Stephen J. Leybourne & Paul Newbold, 2004. "Asymptotic mean‐squared forecast error when an autoregression with linear trend is fitted to data generated by an I(0) or I(1) process," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 583-602, July.
    3. Evan F. Koenig & Sheila Dolmas & Jeremy Piger, 2003. "The Use and Abuse of Real-Time Data in Economic Forecasting," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 618-628, August.
    4. Kirstin Hubrich & David F. Hendry, 2005. "Forecasting Aggregates by Disaggregates," Computing in Economics and Finance 2005 270, Society for Computational Economics.
    5. Andrea Silvestrini & David Veredas, 2008. "Temporal Aggregation Of Univariate And Multivariate Time Series Models: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 22(3), pages 458-497, July.
    6. Arnold Zellner, 1978. "Seasonal Analysis of Economic Time Series," NBER Books, National Bureau of Economic Research, Inc, number zell78-1, March.
    7. Ralf Brüggemann & Helmut Lütkepohl, 2006. "A small monetary system for the euro area based on German data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(6), pages 683-702, September.
    8. Beyer, Andreas & Juselius, Katarina, 2010. "Does it matter how aggregates are measured? The case of monetary transmission mechanisms in the euro area," Working Paper Series 1149, European Central Bank.
    9. Víctor Gómez & Félix Aparicio‐Pérez, 2009. "A new state–space methodology to disaggregate multivariate time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 97-124, January.
    10. Bosker, E.M., 2006. "On the aggregation of eurozone data," Economics Letters, Elsevier, vol. 90(2), pages 260-265, February.
    11. Yamamoto, Taku, 1980. "On the Treatment of Autocorrelated Errors in the Multiperiod Prediction of Dynamic Simultaneous Equation Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(3), pages 735-748, October.
    12. Andreas Beyer & Katarina Juselius, 2008. "Does it Matter How to Measure Aggregates? The Case of Monetary Transmission Mechanisms in the Euro Area," Discussion Papers 08-07, University of Copenhagen. Department of Economics.
    13. Gregory C. Reinsel & Sung K. Ahn, 1992. "Vector Autoregressive Models With Unit Roots And Reduced Rank Structure:Estimation. Likelihood Ratio Test, And Forecasting," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(4), pages 353-375, July.
    14. Daniel O. Stram & William W. S. Wei, 1986. "Temporal Aggregation In The Arima Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(4), pages 279-292, July.
    15. Heather Anderson & Mardi Dungey & Denise Osborn & Farshid Vahid, 2007. "Constructing Historical Euro Area Data," Money Macro and Finance (MMF) Research Group Conference 2006 99, Money Macro and Finance Research Group.
    16. Lutkepohl, Helmut, 1985. "The joint asymptotic distribution of multistep prediction errors of estimated vector autoregressions," Economics Letters, Elsevier, vol. 17(1-2), pages 103-106.
    17. Marcellino, Massimiliano & Stock, James H. & Watson, Mark W., 2003. "Macroeconomic forecasting in the Euro area: Country specific versus area-wide information," European Economic Review, Elsevier, vol. 47(1), pages 1-18, February.
    18. Ralf Brüggemann & Helmut Lütkepohl, 2005. "Uncovered Interest Rate Parity and the Expectations Hypothesis of the Term Structure: Empirical Results for the U.S. and Europe," SFB 649 Discussion Papers SFB649DP2005-035, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    19. Weiss, Andrew A., 1984. "Systematic sampling and temporal aggregation in time series models," Journal of Econometrics, Elsevier, vol. 26(3), pages 271-281, December.
    20. Lorenzo Pascual & Juan Romo & Esther Ruiz, 2004. "Bootstrap predictive inference for ARIMA processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 449-465, July.
    21. Tommaso Proietti & Filippo Moauro, 2006. "Dynamic factor analysis with non‐linear temporal aggregation constraints," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(2), pages 281-300, April.
    22. Palm, Franz C & Nijman, Theo E, 1984. "Missing Observations in the Dynamic Regression Model," Econometrica, Econometric Society, vol. 52(6), pages 1415-1435, November.
    23. Helmut Lütkepohl & Fang Xu, 2012. "The role of the log transformation in forecasting economic variables," Empirical Economics, Springer, vol. 42(3), pages 619-638, June.
    24. Lutkepohl, Helmut, 1981. "A model for non-negative and non-positive distributed lag functions," Journal of Econometrics, Elsevier, vol. 16(2), pages 211-219, June.
    25. Hubrich, Kirstin, 2005. "Forecasting euro area inflation: Does aggregating forecasts by HICP component improve forecast accuracy?," International Journal of Forecasting, Elsevier, vol. 21(1), pages 119-136.
    26. Clements,Michael & Hendry,David, 1998. "Forecasting Economic Time Series," Cambridge Books, Cambridge University Press, number 9780521634809, January.
    27. Beyer, Andreas & Doornik, Jurgen A & Hendry, David F, 2001. "Constructing Historical Euro-Zone Data," Economic Journal, Royal Economic Society, vol. 111(469), pages 102-121, February.
    28. Harvey, Andrew, 2006. "Forecasting with Unobserved Components Time Series Models," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 7, pages 327-412, Elsevier.
    29. Reinsel, Gregory C. & Lewis, Richard A., 1987. "Prediction mean square error for non-stationary multivariate time series using estimated parameters," Economics Letters, Elsevier, vol. 24(1), pages 57-61.
    30. Kemp, Gordon C.R., 1999. "The Behavior Of Forecast Errors From A Nearly Integrated Ar(1) Model As Both Sample Size And Forecast Horizon Become Large," Econometric Theory, Cambridge University Press, vol. 15(2), pages 238-256, April.
    31. Kim, Jae H., 1999. "Asymptotic and bootstrap prediction regions for vector autoregression," International Journal of Forecasting, Elsevier, vol. 15(4), pages 393-403, October.
    32. Hoque, Asraul & Magnus, Jan R. & Pesaran, Bahram, 1988. "The exact multi-period mean-square forecast error for the first-order autoregressive model," Journal of Econometrics, Elsevier, vol. 39(3), pages 327-346, November.
    33. Ralf Brüggemann & Helmut Lütkepohl & Massimiliano Marcellino, 2008. "Forecasting euro area variables with German pre-EMU data," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(6), pages 465-481.
    34. Baillie, Richard T, 1981. "Prediction from the Dynamic Simultaneous Equation Model with Vector Autoregressive Errors," Econometrica, Econometric Society, vol. 49(5), pages 1331-1337, September.
    35. Masarotto, Guido, 1990. "Bootstrap prediction intervals for autoregressions," International Journal of Forecasting, Elsevier, vol. 6(2), pages 229-239, July.
    36. Paul Kabaila, 1993. "On Bootstrap Predictive Inference For Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(5), pages 473-484, September.
    37. William W. S. Wei, 1978. "Some Consequences of Temporal Aggregation in Seasonal Time Series Models," NBER Chapters, in: Seasonal Analysis of Economic Time Series, pages 433-448, National Bureau of Economic Research, Inc.
    38. Angelini, Elena & Marcellino, Massimiliano, 2011. "Econometric analyses with backdated data: Unified Germany and the euro area," Economic Modelling, Elsevier, vol. 28(3), pages 1405-1414, May.
    39. Lewis, Richard & Reinsel, Gregory C., 1985. "Prediction of multivariate time series by autoregressive model fitting," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 393-411, June.
    40. Brewer, K. R. W., 1973. "Some consequences of temporal aggregation and systematic sampling for ARMA and ARMAX models," Journal of Econometrics, Elsevier, vol. 1(2), pages 133-154, June.
    41. Stock, James H, 1996. "VAR, Error Correction and Pretest Forecasts at Long Horizons," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 58(4), pages 685-701, November.
    42. Clements, Michael P. & Taylor, Nick, 2001. "Bootstrapping prediction intervals for autoregressive models," International Journal of Forecasting, Elsevier, vol. 17(2), pages 247-267.
    43. Jörg Breitung & Norman R. Swanson, 2002. "Temporal aggregation and spurious instantaneous causality in multiple time series models," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(6), pages 651-665, November.
    44. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2006. "Predicting volatility: getting the most out of return data sampled at different frequencies," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 59-95.
    45. Lutkepohl, Helmut, 1986. "Forecasting Vector ARMA Processes with Systematically Missing Observations," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(3), pages 375-390, July.
    46. Tiao, G. C. & Guttman, Irwin, 1980. "Forecasting contemporal aggregates of multiple time series," Journal of Econometrics, Elsevier, vol. 12(2), pages 219-230, February.
    47. SBRANA, Giacomo & SILVESTRINI, Andrea, 2009. "What do we know about comparing aggregate and disaggregate forecasts?," LIDAM Discussion Papers CORE 2009020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    48. Sampson, Michael, 1991. "The Effect of Parameter Uncertainty on Forecast Variances and Confidence Intervals for Unit Root and Trend Stationary Time-Series Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(1), pages 67-76, Jan.-Marc.
    49. Engle, Robert F. & Yoo, Byung Sam, 1987. "Forecasting and testing in co-integrated systems," Journal of Econometrics, Elsevier, vol. 35(1), pages 143-159, May.
    50. Marcellino, Massimiliano, 1999. "Some Consequences of Temporal Aggregation in Empirical Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(1), pages 129-136, January.
    51. Fagan, Gabriel & Henry, Jerome & Mestre, Ricardo, 2005. "An area-wide model for the euro area," Economic Modelling, Elsevier, vol. 22(1), pages 39-59, January.
    52. Grigoletto, Matteo, 1998. "Bootstrap prediction intervals for autoregressions: some alternatives," International Journal of Forecasting, Elsevier, vol. 14(4), pages 447-456, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Stylianos Asimakopoulos & Joan Paredes & Thomas Warmedinger, 2020. "Real‐Time Fiscal Forecasting Using Mixed‐Frequency Data," Scandinavian Journal of Economics, Wiley Blackwell, vol. 122(1), pages 369-390, January.
    2. Lütkepohl Helmut, 2011. "Forecasting Nonlinear Aggregates and Aggregates with Time-varying Weights," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 231(1), pages 107-133, February.
    3. Blazej Mazur, 2015. "Density forecasts based on disaggregate data: nowcasting Polish inflation," Dynamic Econometric Models, Uniwersytet Mikolaja Kopernika, vol. 15, pages 71-87.
    4. Brüggemann, Ralf & Lütkepohl, Helmut, 2013. "Forecasting contemporaneous aggregates with stochastic aggregation weights," International Journal of Forecasting, Elsevier, vol. 29(1), pages 60-68.
    5. Ferrara, Laurent & Marsilli, Clément & Ortega, Juan-Pablo, 2014. "Forecasting growth during the Great Recession: is financial volatility the missing ingredient?," Economic Modelling, Elsevier, vol. 36(C), pages 44-50.
    6. Ronayne, David, 2011. "Which Impulse Response Function?," The Warwick Economics Research Paper Series (TWERPS) 971, University of Warwick, Department of Economics.
    7. Hassler, Uwe, 2011. "Estimation of fractional integration under temporal aggregation," Journal of Econometrics, Elsevier, vol. 162(2), pages 240-247, June.
    8. Sbrana, Giacomo & Silvestrini, Andrea, 2013. "Forecasting aggregate demand: Analytical comparison of top-down and bottom-up approaches in a multivariate exponential smoothing framework," International Journal of Production Economics, Elsevier, vol. 146(1), pages 185-198.
    9. Warmedinger, Thomas & Paredes, Joan & Asimakopoulos, Stylianos, 2013. "Forecasting fiscal time series using mixed frequency data," Working Paper Series 1550, European Central Bank.
    10. Jing Zeng, 2016. "Combining country-specific forecasts when forecasting Euro area macroeconomic aggregates," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 43(2), pages 415-444, May.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Andrea Silvestrini & David Veredas, 2008. "Temporal Aggregation Of Univariate And Multivariate Time Series Models: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 22(3), pages 458-497, July.
    2. Sbrana, Giacomo & Silvestrini, Andrea, 2013. "Aggregation of exponential smoothing processes with an application to portfolio risk evaluation," Journal of Banking & Finance, Elsevier, vol. 37(5), pages 1437-1450.
    3. Foroni, Claudia & Marcellino, Massimiliano & Schumacher, Christian, 2011. "U-MIDAS: MIDAS regressions with unrestricted lag polynomials," Discussion Paper Series 1: Economic Studies 2011,35, Deutsche Bundesbank.
    4. Jing Zeng, 2015. "Combining Country-Specific Forecasts when Forecasting Euro Area Macroeconomic Aggregates," Working Paper Series of the Department of Economics, University of Konstanz 2015-11, Department of Economics, University of Konstanz.
    5. Ralf Brüggemann & Jing Zeng, 2015. "Forecasting Euro-Area Macroeconomic Variables Using a Factor Model Approach for Backdating," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 77(1), pages 22-39, February.
    6. Nicholas Taylor, 2008. "The predictive value of temporally disaggregated volatility: evidence from index futures markets," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(8), pages 721-742.
    7. Gonçalves Mazzeu, Joao Henrique & Ruiz Ortega, Esther & Veiga, Helena, 2015. "Model uncertainty and the forecast accuracy of ARMA models: A survey," DES - Working Papers. Statistics and Econometrics. WS ws1508, Universidad Carlos III de Madrid. Departamento de Estadística.
    8. SILVESTRINI, Andrea & VEREDAS, David, 2005. "Temporal aggregation of univariate linear time series models," LIDAM Discussion Papers CORE 2005059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Brüggemann, Ralf & Lütkepohl, Helmut, 2013. "Forecasting contemporaneous aggregates with stochastic aggregation weights," International Journal of Forecasting, Elsevier, vol. 29(1), pages 60-68.
    10. Mamingi Nlandu, 2017. "Beauty and Ugliness of Aggregation over Time: A Survey," Review of Economics, De Gruyter, vol. 68(3), pages 205-227, December.
    11. Helmut Lütkepohl, 2013. "Vector autoregressive models," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 6, pages 139-164, Edward Elgar Publishing.
    12. Anderson, Heather M. & Dungey, Mardi & Osborn, Denise R. & Vahid, Farshid, 2011. "Financial integration and the construction of historical financial data for the Euro Area," Economic Modelling, Elsevier, vol. 28(4), pages 1498-1509, July.
    13. Heather Anderson & Mardi Dungey & Denise Osborn & Farshid Vahid, 2007. "Constructing Historical Euro Area Data," Money Macro and Finance (MMF) Research Group Conference 2006 99, Money Macro and Finance Research Group.
    14. Giacomo Sbrana & Andrea Silvestrini, 2012. "Temporal aggregation of cyclical models with business cycle applications," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(1), pages 93-107, March.
    15. Ramirez, Octavio A., 2011. "Conclusive Evidence on the Benefits of Temporal Disaggregation to Improve the Precision of Time Series Model Forecasts," Faculty Series 113520, University of Georgia, Department of Agricultural and Applied Economics.
    16. Ralf Brüggemann & Helmut Lütkepohl & Massimiliano Marcellino, 2008. "Forecasting euro area variables with German pre-EMU data," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(6), pages 465-481.
    17. Hassler, Uwe, 2011. "Estimation of fractional integration under temporal aggregation," Journal of Econometrics, Elsevier, vol. 162(2), pages 240-247, June.
    18. Jing Zeng, 2016. "Combining country-specific forecasts when forecasting Euro area macroeconomic aggregates," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 43(2), pages 415-444, May.
    19. De Gooijer, Jan G. & Hyndman, Rob J., 2006. "25 years of time series forecasting," International Journal of Forecasting, Elsevier, vol. 22(3), pages 443-473.
    20. repec:hal:journl:peer-00815563 is not listed on IDEAS
    21. Nijman, Theo E & Palm, Franz C, 1990. "Predictive Accuracy Gain from Disaggregate Sampling in ARIMA Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(4), pages 405-415, October.

    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:oec:stdkab:5km399r2jz9n. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/oecddfr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.