I. Introduction
Convergence in global alcohol consumption patterns is an active research area (Smith and Mitry, Reference Smith and Mitry2007; Aizenman and Brooks, Reference Aizenman and Brooks2008; Colen and Swinnen, Reference Colen and Swinnen2016; Holmes and Anderson, Reference Holmes and Anderson2017), as is how to measure convergence in alcohol consumption patterns (Mills, Reference Mills2018). For large diverse markets like the United States, there is also interest in the converse question: why do consumption differences persist (Hart and Alston, Reference Hart and Alston2019). Finally, in addition to measuring historical trends, there has been some research for the United States that has presented forecasts of future alcohol consumption patterns to test whether further convergence in alcohol consumption patterns is likely (Fogarty and Voon, Reference Fogarty and Voon2018). The extension of the convergence literature to consider future possible consumption patterns raises the question of how alcohol consumption forecasts should be developed. The Autoregressive Integrated Moving Average Model (ARIMA) approach used in Fogarty and Voon is just one possible method for developing alcohol consumption forecasts, and there are strong reasons to suspect that averaging across different forecasts will lead to an improvement in forecast accuracy (Bates and Granger, Reference Bates and Granger1969; Clemen, Reference Clemen1989). Further, it is also possible to think of alcohol consumption data as hierarchical time series data, where beer, wine, and spirit consumption must add up to total alcohol consumption. For hierarchical time series data, it is possible to impose additional restrictions to ensure consistency in adding up.
In this note we: (i) show how the R software platform can be used to obtain alcohol consumption forecasts using a range of different methods and (ii) show that no single forecast approach dominates other methods in terms of forecast performance. To illustrate each method, we use the LaVallee, Kim, and Yi (Reference LaVallee, Kim and Yi2014) per capita state level consumption data for the United States.
II. Comparison Setup
The estimation approaches considered are: (i) single equation ARIMA (Box–Jenkins) models (Box et al., Reference Box, Jenkins, Reinsel and Ljung2015); (ii) hierarchical ARIMA models (Hyndman et al., Reference Hyndman, Ahmed, Athanasopoulos and Shang2011); (iii) single equation state space models (exponential smoothing family) (Hyndman et al., Reference Hyndman, Koehler, Ord and Snyder2008); (iv) hierarchical state space models (Hyndman et al., Reference Hyndman, Ahmed, Athanasopoulos and Shang2011); (v) the BATS model of De Livera, Hyndman, and Snyder (Reference De Livera, Hyndman and Snyder2011), which extends traditional state space models to allow for complex seasonality through the introduction of a Box–Cox transformation and ARMA errors;Footnote 1 and (vi) a neural network model of the form detailed in Hyndman and Athanasopoulos (Reference Hyndman and Athanasopoulos2018, Ch. 11). For estimation we rely on two R packages: Hyndman (Reference Hyndman2017) and Hyndman et al. (Reference Hyndman, Lee, Wang and Wickramasuriya2018).
In this application our focus is to compare the performance of different forecast approaches, and so we separate the data set into a training set (1970 to 2007) and a test set (2008 to 2012). For each type of forecasting method we choose the model form that minimizes AIC, over the training set, and then compare model performance using RMSE across the test set. Figure 1 provides an overview of how to apply each forecasting method in R, and the supplementary material provides complete worked examples for each forecast method listed in Figure 1.
Figure 1 Forecasting Alcohol Consumption with R
III. Results
The first approach used to compare forecast method performance is a series of violin plots of RMSE values, where RMSE values are grouped by estimation method and beverage type. The take home messages from Figure 2 are: (i) in terms of RMSE, relatively simple forecast models perform at least as well as more complex models; (ii) for a given beverage type, forecast models appear to have similar performance; and (iii) across all forecast model types, wine forecasts tend to be the most accurate and beer forecasts least accurate.
Figure 2 Violin Plots Comparing Model Performance
Figure 3 plots the maximum and minimum RMSE value for each state by beverage combination across the six forecast methods, and the plots show that there is significant variation in forecast performance between methods across the various state by beverage combinations. Although the plots place the variation in model performance in perspective, they do not show whether one forecast method systematically out performs, when forecasting future alcohol consumption.
Figure 3 Within State Variation in Model Performance: RMSE Comparison
To provide a measure of the relative performance of each forecast method, for each state and beverage, the method with the lowest RMSE was identified, and the information is summarized in Table 1. As can be seen from Table 1, at the individual beverage level, the approach that, on most occasions, minimized RMSE, varied with beverage type. For spirits the forecast method that most often minimized RSME was BATS; for wine it was the single equation ARIMA method; and for beer it was the autoregressive neural network method. As can be seen from the final column of Table 1, performance across forecast methods, in terms of minimizing RMSE, is quite similar. We do not place special emphasis on particular threshold values for Type I errors, and so with p = 0.06 for a proportions test of equality across methods, we simply conclude that there is no strong evidence that one specific forecast method systematically outperforms another, when forecasting future alcohol consumption.
Table 1 Convergence Measures: Coefficient of Variation and Trace
Note: If tied each method allocated 0.5.
To understand the extent of the differences in forecast consumption levels for each beverage type across methods, the five-year-out forecast values for each method, along with the actual value (black dash), are plotted in Figure 4. As can be seen, there is considerable variation in the forecast level of consumption, across models, and presenting these different forecasts can help place forecast uncertainty in perspective. For the five-year-out forecast values, the average difference between the maximum forecast value and the minimum forecast value across methods, expressed as a percentage of the actual consumption level, was 12.5% for spirits (SD 6.4%), 11.1% for wine (SD 6.9%), and 5.1% for beer (SD 4.1). So the variation in long range forecasts across methods is non-trivial.
Figure 4 Five Year Future Forecast Comparison: Per Capita Ethanol Consumption
IV. Conclusion
Forecasting future alcohol consumption values allows a range of interesting hypotheses to be considered. Recent work published in the Journal of Wine Economics has focused on developing alcohol consumption forecasts using the ARIMA method. In this Note we highlight a range of alternative forecast methods that perform at least as well as the ARIMA method, and show how these methods can be implemented in R. To facilitate the use of these methods, a worked example file is provided as part of the supplementary material.
Supplementary Material
For supplementary material accompanying this paper visit https://doi.org/10.1017/jwe.2019.15.
