_GLOBAL FOOD INSECURITY OUTLOOK_ _13_ observed intervals in the post 2019 data, something a simple cross-validation exercise using the 2015-2019 data would not reveal. The application will show that the synthetic data strategy increases prediction performance tremendously on holdout data selected around the edges of the sample space.

One important parameter in the synthetic data algorithm is the cutoff year that determines how many synthetic cases should be added, 1999 being all synthetic data and 2015 being no synthetic data. The synthetic cases are generated with a model that uses all 1999-2019 data, but the final forecast model may not necessarily benefit from training on the full synthetic history. The deeper history on the one hand allows the model to learn a richer representation of the data, but on the other hand the deeper history is more difficult to predict by the imputation model and so the quality of the synthetic cases may be lower. To find the right cut-off, holdout predictions of the final prediction model using all synthetic data cutoff years 1999 _,_ 2000 _, ...,_ 2015 have been validated. The optimal cutoff was selected as 2005, which thus covers synthetic cases leading up to and following the previous global food crisis around 2008.

# **III. Results**

# _A. Validation Results_

Three main models are estimated. _Linear_ uses a simple linear regression, trained only on observed data, thus without addition of any synthetic cases. _Cubist_ trains a Cubist regression on the same original data. _Cubistsynth_ estimates the Cubist regression with synthetic cases. Prediction performance is estimated using several setups. In all the experiments, the models are optimized for R<sup>2</sup> and the associated MAE and RMSE are given for completeness.<sup>16</sup> First a standard 10-fold cross-validation exercise was performed. This application estimates each model 10 times on a 90% sample so that predictions are validated 10 times on the 10% held out observations. The results show that the Cubist model beats the linear model by a large margin, with an R<sup>2</sup> of 0 _._ 94 versus one of 0 _._ 60 for the linear regression, highlighting the nonlinear nature of the data relationships. The linear model is simply not able to cope with the cross-country heterogeneity and nonlinearity.<sup>17</sup> The Cubist model with synthetic cases performs even better. The cross-validated R<sup>2</sup> is 0.95 for the Cubist model with synthetic data, and the RMSE and MAE drop from respectively 3.49 and 1.75 to 3.10 and 1.62 compared to the vanilla Cubist model, approximately a reduction of 10%.

> 16Cubist models can be optimized using two tuning parameters _Committees_ and _Neighbors_ that respectively control the boosting iterations and the degree of neighborhood smoothing that is applied. First a full search across all possible _Neighbor_ values was conducted using the standard grid of boosting iterations (1 _,_ 10 _,_ 20) considered by the implementation of Kuhn et al. (2012). Then, the optimal _Neighbor_ + _/ −_ 1 was used and a boosting grid of 1 _,_ 10 _,_ 20 _,_ 40 _,_ 60 was used. The maximum number of boosting iterations possible is 100 but this increased computational burden beyond manageable levels.

> 17A fixed effects model may cope better with the cross-country heterogeneity but would not be able to