Abstract
In this chapter, we introduce readers to the concept of ensemble forecast models. Developed in the late 1960s, this method has become well accepted in the literature on economic forecasting. It involves combining different single forecasts into a combined forecast. Ensemble models have been shown to have better prediction accuracy (lower forecast error variance) than single forecasts in the forecasting of economic and financial variables. We examine this technique using data on sales tax revenue for the city of Chicago from 1982 to 2016. We find that for five years of pseudo-out-of-sample forecasts, ensemble models demonstrated better overall forecast accuracy, while some single forecasts did very well in specific years.
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Notes
- 1.
Although many sources cite the field of meteorology as coming up with the specific term, the theory and logic around combining forecasts seems to have developed in parallel in meteorological and economic/financial forecasting.
- 2.
The superscript BG refers to the Bates-Granger weighting method. As we will be evaluating many individual and combination forecasts we will refer to them by initials.
- 3.
The logic of these type of models is that the weight reflects the posterior probability that the ith forecast model has the lowest error variance among all N models.
- 4.
We include national- and state-level variables due to a paper by Chudik et al. (2017) who show that economic activity at lower levels of population aggregation (state and local levels) are often influenced by higher-level economic conditions. State gross domestic product data is also available, but it starts in 1997, providing too few in-sample observations for model development.
- 5.
We also estimated a VAR with the same variables as VAR1 except for national GDP instead of national personal income as an exogenous variable. The results were nearly identical to VAR1.
- 6.
The Excel file and STATA results are available on request.
- 7.
We also calculated the mean square prediction error (MPSE) for the models. There were no qualitative differences in the results except that the simple average weighting method no longer was better than the best single model. Full results including weights and procedures available from the author.
- 8.
Thanks to Dr. John Mikesell, who commented on a presentation of an earlier draft at the 2018 ABFM Conference, for the suggestion to use this method of comparison.
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Kriz, K.A. (2019). Ensemble Forecasting. In: Williams, D., Calabrese, T. (eds) The Palgrave Handbook of Government Budget Forecasting. Palgrave Studies in Public Debt, Spending, and Revenue. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-030-18195-6_21
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DOI: https://doi.org/10.1007/978-3-030-18195-6_21
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