CSAR: the cross-sectional autoregression model for short and long-range forecasting

  • Claudio HartmannEmail author
  • Franziska Ressel
  • Martin Hahmann
  • Dirk Habich
  • Wolfgang Lehner
Regular Paper


The forecasting of time series data is an integral component for management, planning, and decision making. Following the Big Data trend, large amounts of time series data are available in many application domains. The highly dynamic and often noisy character of these domains in combination with the logistic problems of collecting data from a large number of data sources imposes new requirements on the forecast process. A constantly increasing number of time series has to be forecast over several periods in order to enable long-term planning with high accuracy and short execution time. This is almost impossible, when keeping the traditional focus on creating one forecast model for each individual time series. In addition, often used forecast techniques like ARIMA require complete historical data and fail if time series are intermittent. A method that addresses all these new requirements is the cross-sectional forecasting approach. It utilizes available data from many time series of the same domain in one single model; thus, missing values can be compensated and accurate forecast results are calculated quickly. However, this approach is limited by a rigid data selection and existing forecast methods show that adaptability of the model to the data increases the forecast accuracy. Therefore in this paper, we present CSAR, a model that extends the cross-sectional paradigm by adding more flexibility and allows fine-grained adaptations toward the analyzed data. In this way, we achieve an increased forecast accuracy and thus a wider applicability.


Time series analysis Large-scale time series data Long-range forecasting Multivariate time series 



  1. 1.
    Aldrin, M., Damsleth, E.: Forecasting non-seasonal time series with missing observations. J. Forecast. 8(2), 97–116 (1989). CrossRefGoogle Scholar
  2. 2.
    Bemdt, D.J., Clifford, J.: Using dynamic time warping to find patterns in time series. In: AAAIWS’94 Proceedings of the 3rd International Conference on Knowledge Discovery and Data Mining, pp. 359–370 (1994)Google Scholar
  3. 3.
    Box, G.E.P., Jenkins, G.M., Reinsel, G.C.: Time Series Analysis: Forecasting and Control (Wiley Series in Probability and Statistics). Wiley, New York (2008)CrossRefzbMATHGoogle Scholar
  4. 4.
    Chatfield, C.: Time-Series Forecasting. Chapman & Hall/CRC Press, Boca Raton (2000)CrossRefGoogle Scholar
  5. 5.
    Croston, J.D.: Forecasting and stock control for intermittent demands. Oper. Res. Q. 23(3), 289–303 (1972). CrossRefzbMATHGoogle Scholar
  6. 6.
    Fliedner, G.: Hierarchical forecasting: issues and use guidelines. Ind. Manag. Data Syst. 101(1), 5–12 (2001). CrossRefGoogle Scholar
  7. 7.
    Friedman, J.H.: Multivariate adaptive regression splines. Ann. Stat. 19(1), 1–67 (1991). MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Friedman, J.H.: Greedy function approximation: a gradient boosting machine. Ann. Stat. 29(5), 1189–1232 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    GOFLEX Project. (11.02.2017)
  10. 10.
    Hartmann, C., Hahmann, M., Habich, D., Lehner, W.: CSAR: The Cross-sectional autoregression model. In: 2017 International Conference on Data Science and Advanced Analytics (DSAA 2017), Tokyo, pp. 1–10 (2017)Google Scholar
  11. 11.
    Hartmann, C., Hahmann, M., Rosenthal, F., Lehner, W.: Exploiting big data in time series forecasting : a cross-sectional approach. In: IEEE International Conference on Data Science and Advanced Analytics (DSAA), 2015, Paris, pp. 1–10 (2015).
  12. 12.
    Holt, C.C.: Forecasting seasonals and trends by exponentially weighted moving averages. Int. J. Forecast. 20(1), 5–10 (2004). CrossRefGoogle Scholar
  13. 13.
    Hyndman, R.J., Khandakar, Y.: Automatic time series for forecasting: the forecast package for R. J. Stat. Softw. 27(3), 1–22 (2008)CrossRefGoogle Scholar
  14. 14.
    IJCAI: IJCAI 2017 - Data Mining Contest (08.02.2017).
  15. 15.
    Irish Social Science Data Archive (ISSDA): CER Smart Metering Project. The Commission for Energy Regulation (CER) (28.04.2015).
  16. 16.
    Levy, D.: Introduction to Numerical Analysis (2010)Google Scholar
  17. 17.
    McCarthy, T.M., Davis, D.F., Golicic, S.L., Mentzer, J.T.: The evolution of sales forecasting management: a 20-year longitudinal study of forecasting practices. J. Forecast. 25(5), 303–324 (2006). MathSciNetCrossRefGoogle Scholar
  18. 18.
    Neupane, B., Pedersen, T.B., Thiesson, B.: Towards flexibility detection in device-level energy consumption. In: Woon, W.L., Aung, Z., Madnick, S. (eds.) Data Analytics for Renewable Energy Integration: Proceedings of the Second ECML PKDD Workshop, DARE 2014, vol. 8817, Nancy, pp. 1–16 (2014).
  19. 19.
    R Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria (2014).
  20. 20.
    Riise, T., Tjostheim, D.: Theory and practice of multivariate arma forecasting. J. Forecast. 3(3), 309–317 (1984). CrossRefGoogle Scholar
  21. 21.
    Robert, N.: Statistical forecasting: notes on regression and time series analysis. Accessed 09.11.2016
  22. 22.
    Shenstone, L., Hyndman, R.J.: Stochastic models underlying Croston’s method for intermittent demand forecasting. J. Forecast. 24(6), 389–402 (2005)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Tiao, G.C., Box, G.E.P.: Modeling multiple time series with applications. J. Am. Stat. Assoc. 76(376), 802–816 (1981). MathSciNetzbMATHGoogle Scholar
  24. 24.
    Universal Smart Energy Framework (USEF). (11.02.2017)
  25. 25.
    VDE Verband der Elektrotechnik Elektronik Informationstechnik e.V.: Messwesen Strom (Metering Code); VDE-AR-N 4400 (2011)Google Scholar
  26. 26.
    Vermesan, O., Friess, P.: Internet of Things: Converging Technologies for Smart Environments and Integrated Ecosystems. River Publishers, Aalborg (2013)Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Database Systems GroupTechnische Universität DresdenDresdenGermany

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