Modeling and forecasting small national eco-efficiency time series
Sustainable development. Environmental and economic impacts. Window Data Envelopment Analysis. Machine learning algorithms.
Eco-efficiency time series are useful for monitoring the relationship between economic and environmental variables. However, national eco-efficiency time series are mostly small or very small. Therefore, specific strategies are needed to model and forecast these types of series.In this context, the objective of this research is to study a method for modeling and forecasting national eco-efficiency time series. In turn, to obtain national eco-efficiency time series, Data Envelopment Analysis combined with Window Analysis (WDEA) is applied. To calculate the window size in WDEA, a method based on the divergence of eco-efficiency is proposed. In particular, the ideal window width is the one that maximizes the eco-efficiency dispersion. To model the national eco-efficiency time series, two strategies are considered: (i) individual time series; and (ii) pooled approaches. In the former, the usual way of dealing with each univariate time series is considered. The latter case consists of pooling the univariate time series of territories, considering individual effects of each country and lags. Machine learning single models for time series are adopted in both cases: Support Vector Regression (SVR), Long Short-Term Memory (LSTM), Decision Tree Regression (DTR); and ensemble: combination by Simple Average (SA), Simple Median (SM), Minimum Variance (MV); Random Forest Regression (RFR) and Extreme Gradient Boosting (XGB). Further, considering the individual approach, Autoregressive Integrated Moving Average (ARIMA) and Exponential Smoothing (ETS) are also considered. The Mercosul, BRICS and G18 countries were considered as case studies, involving eco-efficiency time series from 1995 to 2020. The optimal window size is equal to 1, with maximum eco-efficiency dispersion between countries. From three cases studied, pooled approach winning in two (Mercosul and BRICS), with 66.7% of series. Furthermore, ensemble learning wins in 11 (57.9%) of time series. However, in general the models building with pooled structures winning in 42.1% of time series considering. Finally, considering the best models and the 8-year horizon ahead, the average eco-efficiency was predicted to be approximately 0.71, 0.56 and 0.39, for Mercosul, BRICS and G18, respectively. In conclusion, pooled approach can be a good forecasting technique, however improvements are still needed.