Parameter estimation of time series models using Bayesian technique

Abstract

In time series literature, use of exogenous variable(s) in done to enhance the modelling as well as forecasting efficiency of the model. Various models have been proposed in literature and ARIMAX model is one of the preferred choice among the researchers. It is due to its ease of application and wide range of applicability. To deal with inherently noisy data sets such as financial series, its variant ARIMAX-GARCH is widely used. Like all other time series models, ARIMAX and ARIMAX-GARCH models are governed with some assumptions. In some practical applications, these assumptions are hard to satisfy. Under such scenarios one has to seek help of alternate methodologies such as Bayesian estimation technique. Past decade has witnessed unprecedented growth in the evolution of statistical computing. This has paved way for researchers to explore the Bayesian paradigm in time series domain. Further, on concentrated literature search we could find very few applications of these two models in agriculture domain. Also, we were unable to obtain any literature that has applied Bayesian framework for parameter estimation of ARIMAX and ARIMAX-GARCH model. Hence, these two research gaps intrigued us to take up the present investigation and document our findings. We have applied these two models on agricultural data sets and attempted to enrich the Bayesian time series literature by documenting estimation technique of ARIMAX and ARIMAXGARCH model using Bayesian framework. We strongly believe that the proposed models will find wide application in agricultural domain ranging from price forecasting to forecasting rainfall, etc. The product developed in form of R package which is freely accessible will help the researchers working in this field.