GARCH modelling in association with FFT–ARIMA to forecast ozone episodes

In operational forecasting of the surface O₃ by statistical modelling, it is customary to assume the O₃ time series to be generated through a homoskedastic process. In the present work, we’ve taken heteroskedasticity of the O₃ time series explicitly into account and have shown how it resulted in O₃ forecasts with improved forecast confidence intervals. Moreover, it also enabled us to make more accurate probability forecasts of ozone episodes in the urban areas. The study has been conducted on daily maximum O₃ time series for four urban sites of two major European cities, Brussels and London. The sites are: Brussels (Molenbeek) (B1), Brussels (PARL.EUROPE) (B2), London (Brent) (L1) and London (Bloomsbury) (L2). Fast Fourier Transform (FFT) has been used to model the periodicities (annual periodicity is especially distinct) exhibited by the time series. The residuals of “actual data subtracted with their corresponding FFT component” exhibited stationarity and have been modelled using ARIMA (Autoregressive Integrated Moving Average) process. The MAPEs (Mean absolute percentage errors) using FFT–ARIMA for one day ahead 100 out of sample forecasts, were obtained as follows: 20%, 17.8%, 19.7% and 23.6% at the sites B1, B2, L1 and L2. The residuals obtained through FFT–ARIMA have been modelled using GARCH (Generalized Autoregressive Conditional Heteroskedastic) process. The conditional standard deviations obtained using GARCH have been used to estimate the improved forecast confidence intervals and to make probability forecasts of ozone episodes. At the sites B1, B2, L1 and L2, 91.3%, 90%, 70.6% and 53.8% of the times probability forecasts of ozone episodes (for one day ahead 30 out of sample) have correctly been made using GARCH as against 82.6%, 80%, 58.8% and 38.4% without GARCH. The incorporation of GARCH also significantly reduced the no. of false alarms raised by the models.