To combine or not to combine? issues of combining forecasts

International Journal of Forecasting, 2005

Much research shows that combining forecasts improves accuracy relative to individual forecasts. In this paper we present experiments, using the 3003 series of the M3-competition, that challenge this belief: on average across the series, the best individual forecasts, based on post-sample performance, perform as well as the best combinations. However, this finding lacks practical value since it requires that we identify the best individual forecast or combination using post sample data. So we propose a simple model-selection criterion to select among forecasts, and we show that, using this criterion, the accuracy of the selected combinations is significantly better and less variable than that of the selected individual forecasts. These results indicate that the advantage of combining forecasts is not that the best possible combinations perform better than the best possible individual forecasts, but that it is less risky in practice to combine forecasts than to select an individual forecasting method.

Socio-Economic Planning Sciences, 1989

2000

We study some methods of combining procedures for forecasting a continuous random variable. Statistical risk bounds under the square error loss are obtained under mild distributional assumptions on the future given the current outside information and the past observations. The risk bounds show that the combined forecast automatically achieves the best performance among the candidate procedures up to a constant factor and an additive penalty term. In term of the rate of convergence, the combined forecast performs as well as if one knew which candidate forecasting procedure is the best in advance.

Research Papers in Economics, 1998

During the past thirty years, there has been considerable concern about combination of forecasts. Many of the articles and books dedicated to this specific area explain and demonstrate that combining multiple individual forecasts can improve forecast accuracy. The improvement in accuracy mainly depends on forecast combination techniques which range from simple combinations like averaging the forecasts to more complex ones that use the Bayesian approach. This paper provides a bibliography of selected articles and books related to the combination of forecasts in various disciplines and is intended to be a catalog for locating contributions in research areas focusing on the theory and applications of combining forecasts. The bibliography includes recent articles and is as up-to-date as possible.

International Journal of Forecasting, 1989

Research from over 200 studies demonstrates that combining forecasts produces consistent but modest gains in accuracy. However, this research does not define well the conditions under which combining is most effective nor how methods should be combined in each situation. Rule-based forecasting can be used to define these conditions and to specify more effective combinations.

Central European Economic Journal

This study contrasts GARCH models with diverse combined forecast techniques for Commodities Value at Risk (VaR) modeling, aiming to enhance accuracy and provide novel insights. Employing daily returns data from 2000 to 2020 for gold, silver, oil, gas, and copper, various combination methods are evaluated using the Model Confidence Set (MCS) procedure. Results show individual models excel in forecasting VaR at a 0.975 confidence level, while combined methods outperform at 0.99 confidence. Especially during high uncertainty, as during COVID-19, combined forecasts prove more effective. Surprisingly, simple methods such as mean or lowest VaR yield optimal results, highlighting their efficacy. This study contributes by offering a broad comparison of forecasting methods, covering a substantial period, and dissecting crisis and prosperity phases. This advances understanding in financial forecasting, benefiting both academia and practitioners.

Applied Economics Letters, 2007

Econometric Reviews, 2010

When the objective is to forecast a variable of interest but with many explanatory variables available, one could possibly improve the forecast by carefully integrating them. There are generally two directions one could proceed: combination of forecasts (CF) or combination of information (CI). CF combines forecasts generated from simple models each incorporating a part of the whole information set, while CI brings the entire information set into one super model to generate an ultimate forecast. Through analysis and simulation, we show the relative merits of each, particularly the circumstances where forecast by CF can be superior to forecast by CI, when CI model is correctly specified and when it is misspecified, and shed some light on the success of equally weighted CF. In our empirical application on prediction of monthly, quarterly, and annual equity premium, we compare the CF forecasts (with various weighting schemes) to CI forecasts (with methodology mitigating the problem of parameter proliferation such as principal component approach). We find that CF with (close to) equal weights is generally the best and dominates all CI schemes, while also performing substantially better than the historical mean.

2019

Program in Systems Modeling and Analysis Combining multiple forecasts in order to generate a single, more accurate one is a well-known approach. A simple average of forecasts has been found to be robust despite theoretically better approaches, increasing availability in the number of expert forecasts, and improved computational capabilities. The dominance of a simple average is related to the small sample sizes and to the estimation errors associated with more complex methods. We study the role that expert correlation, multiple experts, and their relative forecasting accuracy have on the weight estimation error distribution. The distributions we find are used to identify the conditions when a decision maker can confidently estimate weights versus using a simple average. We also propose an improved expert weighting approach that is less sensitive to covariance estimation error while providing much of the benefit from a covariance optimal weight. These two improvements create a new heuristic for better forecast aggregation that is simple to use. This heuristic appears new to the literature and is shown to perform better than a simple average in a simulation study and by application to xiv economic forecast data.