Vector autoregressive with exogenous variable model and its application in modeling and forecasting energy data: case study of PTBA and HRUM energy

Owing to its simplicity and less restrictions, the vector autoregressive with exogenous variable (VARX) model is one of the statistical analyses frequently used in many studies involving time series data, such as finance, economics, and business. The VARX model can explain the dynamic behavior of the relationship between endogenous and exogenous variables or of that between endogenous variables only. It can also explain the impact of a variable or a set of variables on others through the impulse response function (IRF). Furthermore, VARX can be used to predict and forecast time series data. In this study, PTBA and HRUM energy as endogenous variables and exchange rate as an exogenous variable were studied. The data used herein were collected from January 2014 to October 2017. The dynamic behavior of the data was also studied through IRF and Granger causality analyses. The forecasting data for the next one month was also investigated. On the basis of the data provided by these different models, it was found that VARX (3,0) is the best model to assess the relationship between the variables considered in this work.