A Simple Explanation of the Forecast Combination Puzzle

By Jeremy Smith, K. Wallis. 2009

362 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Management Science and Operations Research, Statistics and Probability

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Citations in the corpus

Combining day-ahead forecasts for British electricity prices (2013, background): “Several studies have shown that, due to the effect of finite-sample error in estimating the combining weights, an equally weightedmean is often the best choice (Clemen, 1989;Makridakis andWinkler, 1983; Smith and Wallis, 2009; Stock and Watson, 2001, 2004).”
To Combine Forecasts or to Combine Information? (2010, background): “The consistent estimation of ̂ p! amounts to the consistent estimation of the forecast combination weight w in Section 3.1 and Smith and Wallis (2008).”
Combining forecasts – forty years later (2011, methodology): “As I have observed (Wallis, 2005), distributions have been aggregated ever since Zarnowitz (1969) published averages of the density forecasts of inflation and Gross National Product (GNP) growth supplied in histogram form by respondents to the ASA-NBER survey of forecasts by economic statisticians (”
Model Averaging and Its Use in Economics (2017, background): “o data adaptivity. This empirical fact that “optimally” estimated weights often perform worse than equal weights in terms of mean squared forecast error is known as the “forecast combination puzzle”. Smith and Wallis (2009) provide an explanation for this phenomenon in terms of the additional uncert”
The Evolution of Forecast Density Combinations in Economics (2018, background): “Management science and risk analysis The combination of predictive densities has received considerable attention within management science and risk analysis dating back, at least, to Winkler (1968); for reviews see Genest and Zidek (1986) and Clemen and Winkler (1999).”
Model Averaging in Economics: An Overview (2015, neutral): “Smith and Wallis (2009)). In theory, if the available forecasts are uncorrelated, the optimal weights under mean squared loss should be inversely proportional to each forecast’s variance. Bates and Granger (1969) suggested using empirical weights based on out-of-sample forecast variances.”
The Forecast Combination Puzzle: A Simple Theoretical Explanation (2016, methodology): “A particularly rigorous attempt to explain the puzzle, using simulations and an empirical example, was undertaken by Smith and Wallis (2009) who showed that the reason lies in the estimation error.”
Some Theoretical Results on Forecast Combinations (2018, positive): “This also corroborates the findings of Smith and Wallis (2009) that the reason for the poor performance of optimal weights relative to taking a simple average in finite sample is tied up with the estimation error generated when estimating the weights.”
An empirical comparison of alternate schemes for combining electricity spot price forecasts (2013, neutral): “This robustness property of the equal weighting scheme is shown, perhaps counter-intuitively, to be expected by Smith and Wallis (2009) when the quality of the individual forecasts is similar.”
Advances in Forecasting Under Instability (2012, neutral): “Possible explanations of why forecast combinations may work well include nite sample error in the weights estimates (see Smith and Wallis, 2009) and di¤erent degrees of mis-speci cations in the forecasting models, as determined by instabilities (see Hendry and Clements, 2004).”
Combining Forecasts: An Application to Elections (2014, neutral): “For example, the National Industrial Conference Board (1963) and Wolfe (1966) recommended combined forecasts.”