Transformed-Arimax Model for Heavy Tailed Distributions

This study develops a Transformed Autoregressive Integrated Moving Average with covariate X by taking the logarithm of Arimax (Log-ARIMAX) model for high frequency time series data that is coupled with external time-varying covariate(s) with heavy tailed distributional lognormal form of a residual structure. This study also evaluates both the in-sample and out-sample forecasting accuracy of two forecasting models namely ARIMAX and Log-ARIMAX. A Log-ARIMAX model for time series data with heavy-tailed trait to analyse the obtained data is proposed. The Generalised Linear Method (GLM) was used to estimate the parameters of the proposed model. The oil spill data used was collected both monthly and yearly and was derived from four Oil and Gas companies from 2005-2020 with a total of 64 observations. The Mean Square Error (MSE), Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) serve as the error metrics (Forecast Accuracy Measures) in evaluating the forecastability of the models. Also, Diebold and Mariano test of Accuracy was employed to test the significance of the models. The results of analysis show that Log-ARIMAX models performed better as compared to ARIMAX models in both time regimes. The study recommended that the Transformed-Arimax model is good for a time series data with heavy tailed distributions.