Modified Box-Jenkins and GARCH for forecasting highly volatile time series data - Siti Roslindar, Yaziz (2019)
The Box-Jenkins model has widely been used either as the forecasting, benchmarking or as the integrated model in the current research of time series. The Box-Jenkins modelling is one of the most powerful forecasting techniques available in research practice of the time series analysis. Most of the time series data such as in economics and in environmental sciences are volatile in nature. However, for a highly volatile time series data, the Box-Jenkins model is inappropriate to be applied since it violates the errors assumption of constant variance and it is not able to handle the heteroscedasticity property. Combining the model with a heteroscedastic stochastic model such as the generalised autoregressive conditional heteroscedastic model (GARCH) can be an effective way to overcome the limitation of the Box-Jenkins model in handling the non-constant variance. This study evaluates the performance of the combination model of Box-Jenkins and GARCH-type in modelling and forecasting univariate highly volatile time series data with Box-Jenkins modelling as the base procedure. In evaluating the performance of the model, four procedures are proposed in this study where the first three procedures are using the model of Box-Jenkins and standard GARCH (or BJ-G). The first proposed procedure is developed based on the theoretical Box-Jenkins’s procedure and it is used for the preliminary study. The second proposed procedure is developed based on the first proposed procedure to focus on handling the highly volatile time series data specifically, using BJ-G model by emphasizing on the identification of highly volatile characteristic in the data at the early stage. While the third proposed procedure is an extension from the second procedure, which evaluates the multistep ahead forecasting performance of the BJ-G model. The fourth procedure of BJ-G is developed from the second and third procedures and it is a comprehensive procedure for modelling and forecasting highly volatile time series data using Box-Jenkins – GARCH-type model. The proposed procedures are illustrated using the daily world gold price data since it is a highly volatile type of time series. Based on the preliminary study on 5000 world daily gold price data set using the first procedure of BJ-G, the small magnitude of error proves that BJ-G is a reliable model in modelling and forecasting highly volatile data. The empirical results of the world daily gold price using the second proposed procedure indicate that the procedure is more practical than the first propose procedure to be used in modelling a univariate highly volatile data using BJ-G model which simultaneously ensures an optimal number of data in dealing with the model. The empirical results suggested that the latest 25% of data or 1250 data is sufficient to be employed using BJ-G model with similar forecasting performance as by using all data. Meanwhile, based on the empirical results on the 1250 world daily gold prices and by employing the third procedure, it is found that the BJ-G model is able to follow the trend of the actual data up to seven days ahead, specifically within 95% prediction interval. The fourth proposed procedure is also tested on the Box-Jenkins with various GARCH-type models using the same data series as in the third proposed procedure. In conclusion, the combination model of Box-Jenkins and GARCH-type has great potential, thus the fourth proposed procedure of BJ-G provides a comprehensive, systematic and practical procedure of time series forecasting for univariate highly volatile time series data.