Location of Repository

A Hierarchical Procedure for the Combination of Forecasts ; This is a revised version of Working Paper 228, Economics Series, October 2008, which includes some changes. The most important change regards the reference of Kisinbay (2007), which was not reported in the previous version. The hierarchical procedure proposed in the paper is based on the approach of Kisinbay (2007), but some modifications of that approach are provided.

By Mauro Costantini and Carmine Pappalardo


This paper proposes a strategy to increase the efficiency of forecast combination. Given the availability of a wide range of forecasts for the same variable of interest, our goal is to apply combining methods to a restricted set of models. To this aim, a hierarchical procedure based on an encompassing test is developed. Firstly, forecasting models are ranked according to a measure of predictive accuracy (RMSFE). The models are then selected for combination such that each forecast is not encompassed by any of the competing forecasts. Thus, the procedure aims to unit model selection and model averaging methods. The robustness of the procedure is investigated in terms of the relative RMSFE using ISAE (Institute for Studies and Economic Analyses) short-term forecasting models for monthly industrial production in Italy.Combining forecasts, Econometric models, Evaluating forecasts, Models selection, Time series

OAI identifier:

Suggested articles



  1. (2007). A look into the factor model black box -publication lags and the role of hard and soft data in forecasting GDP, Working Paper Series 751, European Central Bank.
  2. (2004). Combination forecasts of output growth in a seven-country data set.
  3. (1987). Combining forecasts to improve earnings per share prediction: and examination of electric utilities.
  4. (1995). Comparing Predictive Accuracy.
  5. (2001). Computer automation of general-tospeci¯c model selection procedures.
  6. (2002). Determining the Number of Factors in Approximate Factor Models.
  7. (2000). Energy consumption, survey data and the prediction of industrial production in Italy: a comparison and combination of di®erent models,
  8. (2002). Forecast Combination and Encompassing. In:
  9. (2004). Forecasting industrial production and the early detection of turning points.
  10. (1991). Forecasting the Italian industrial production index in real time,
  11. (1984). Improved Methods of Combining Forecasts.
  12. (1999). Improving on Data mining reconsidered by K.D. Hoover
  13. (2002). Macroeconomic forecasting using di®usion indices.
  14. (1992). Parameter Constancy, Mean Square Forecast Errors, and Measuring Forecast Performance: An Exposition, Extensions, and Illustration.
  15. (1987). Short-term forecasting of the industrial production index,
  16. (1987). Structural Change and the Combination of Forecasts.
  17. (1997). Testing the equality of prediction mean squared errors.
  18. (1998). Tests for forecast encompassing.
  19. (2000). Tests for multiple forecast encompassing,
  20. (2007). The Use of Encompassing Tests for Forecast Combinations. Working paper,

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.