Abstract
Autoregressive integrated moving average with exogenous variable-Generalized autoregressive conditional heteroscedastic (ARIMAX-GARCH) model is employed for describing volatile data by incorporating the exogenous variables in the mean-model. Brief description of this model along with its estimation procedure is discussed. For computing out-of-sample forecast using ARIMAX-GARCH model, one need to compute the out-of-sample forecast of exogenous variable first. In the present investigation, the forecasts for exogenous variable have been obtained by using ARIMA methodology as well as by wavelet analysis in frequency domain. As an illustration, wheat yield in Kanpur district of Uttar Pradesh, India with an exogenous variable as maximum temperature at critical root initiation (CRI) stage of wheat crop during 1972 to 2013 have been considered. The forecast of maximum temperature have been obtained using ARIMA and wavelet methodology. The forecast performance has been compared with respect to relative mean absolute prediction error (RMAPE). Finally forecast of wheat yield has been obtained by ARIMAX, ARIMAX-GARCH and ARIMAX-GARCH-WAVELET models. To this end comparison of forecast performance among above three models was carried out using Diebold-Mariano test along with mean absolute prediction error(MAPE), RMAPE and root mean squares error (RMSE). It is found that ARIMAX-GARCH-WAVELET model outperforms other models as far as modelling and forecasting is concerned.