Empirical study of GARCH models with leverage effect in an environmental application

Atmospheric carbon dioxide concentration (ACDC) level is an important factor for predicting temperature and climate changes. We analyze the conditional variance of a function of ACDC level known as ACDC level growth rate (ACDCGR) using the generalised autoregressive conditional heteroskedasticity (GARCH) and GARCH models with leverage effect. The data are a subset of the well known Mauna Loa atmosphere carbon dioxide record. We test for the presence of stylized facts in the ACDCGR time series. The performance of GARCH models are compared to EGARCH, TGARCH and PGARCH models. Model fit measures AIC, BIC and likelihood is calculated for each fitted model. The results do confirm the presence of some of important stylized facts in the ACDCGR time series, but the presence of leverage effect is not significant . The out of sample one step ahead forecasting performances of the models based on RMSE and MAE metrics are evaluated. EGARCH model with student $t$ disturbances showed the best fit and a valid forecasting performance. A bootstrap algorithm is employed to calculate confidence intervals for future values of ACDCGR time series and its volatility. The constructed bootstrap confidence intervals showed a reasonable performance.