A hybrid model to forecast greenhouse gas emissions in Latin America

Abstract

Climate change is the greatest threat to humanity, with harmful broad-spectrum impacts to human health and the natural environment. One of the main causes of this change is the greenhouse effect caused by greenhouse gases (GHG). To limit the impact of GHG to the environment, it is necessary to control emissions from human-produced sources. To date, 192 out of 197 parties at the Paris Agreement have approved ratification to reduce GHG in their countries. However, to properly control the emissions of GHG, accurate and precise forecasts of emissions are necessary. A wide variety of statistical models, computational intelligence and experience curves have been applied in an attempt to provide both accurate and precise forecasts. In this paper, a hybrid model is proposed that combines a fuzzy autoregressive integrated moving average (FARIMA), a probabilistic neural network (PNN), and an adaptive neuro-fuzzy inference system (ANFIS), where the first two models seek to exceed both the limitations of the ARIMA models (linear behavior and great need for data) and FARIMA (wide forecast ranges) alone. The ANFIS model is applied to the results of the first two to improve the overall accuracy of the models. We apply the proposed model in the context of eight Latin American countries (Argentina, Brazil, Chile, Colombia, Mexico, Paraguay, Peru and Uruguay). The results show improvement with MAE, RMSE and RMSRE reduced by more than 90% against comparison models. Additionally, when using performance indices such as the Willmott index of agreement, values close to 1 are obtained. It is concluded that the proposed hybrid model reduces the forecast interval width and increases the accuracy of the forecast by applying ANFIS, overcoming the results of FARIMA and PNN alone which delivered precise but not accurate results. Finally, emissions are forecast for 2025 and 2050 in the aforementioned countries, observing that GHG emissions increase in the region without adhering to the Paris Agreement commitments, which indicates the importance of these countries taking measures in order to mitigate the emission of greenhouse gases.

Appendices

A time series by Country

See Fig. 4.

Fig. 4

Time series

Table 22 Augmented Dickey-Fuller (ADF) test

Table 23 Ljung-Box (LB) test

B Stationarity and whiteness tests

1.1 Appendix B.1. Augmented dickey-fuller (ADF) test

• H$_0$ The time series has a unit root.

• H$_a$ The time series is stationary (Table 22).

1.2 B. 2 Ljung-Box (LB) test

• H$_0$ The time series are independently distributed (i.e., the correlations in the population from which the sample is taken are 0, so that any observed correlations in the data result from randomness of the sampling process).

• H$_a$ The time series are not independently distributed; they exhibit serial correlation (Table 23).

C Graphics Stage I, on the difference(ln(serie))

For appendices C-G, the ordinate axis represents the difference of the natural logarithm transformation of the time series; LB stands for Lower Bound and UB for Upper Bound (Fig. 5).

Fig. 5

Results stage I

Fig. 6

Results stage II

Fig. 7

Results stage III

Fig. 8

Results stage IV

Fig. 9

Results stage V

Table 24 Forecast bounds, Argentina

Table 25 Forecast bounds, Brazil

Table 26 Forecast bounds, Chile

Table 27 Forecast bounds, Colombia

Table 28 Forecast bounds, Mexico

Table 29 Forecast bounds, Paraguay

Table 30 Forecast bounds, Peru

Table 31 Forecast bounds, Uruguay

D Graphics Stage II, on the difference(ln(serie))

E Graphics stage III, on the difference(ln(serie))

F Graphics Stage IV, on the difference(ln(serie))

G Graphics stage V, on the difference(ln(serie))

H Bounds forecast periods

In the following tables, the abbreviations used are “LB” for Lower Bound, “UB” for Upper Bound and “I,” “II,” “III,” “IV” and “V” for the proposed hybrid model stages (Tables 24, 25, 26, 27, 28, 29, 30, 31).

I Graphics model performance in testing data

For this appendix, the following caption is used, where LB and UB stand for Lower Bound and Upper Bound, respectively.

Fig. 10

Caption for the model performance in testing data

Fig. 11

Model performance in testing data