Comparison of Kullback-Leibler, Hellinger and LINEX with Quadratic Loss Function in Bayesian Dynamic Linear Models: Forecasting of Real Price of Oil

In this paper we intend to examine the application of Kullback-Leibler, Hellinger and LINEX loss function in Dynamic Linear Model using the real price of oil for 106 years of data from 1913 to 2018 concerning the asymmetric problem in filtering and forecasting. We use DLM form of the basic Hoteling Model under Quadratic loss function, Kullback-Leibler, Hellinger and LINEX trying to address the results if we treat the ‘over-estimation’ and ‘under-estimation’ differently. So, we drive one-step-ahead forecast for Dynamic Linear Model under quadratic, LINEX and Kullback-Leibler losses in Bayesian context. With Normal posterior distribution, our results suggest that, the LINEX loss function may provide better forecasts than conventional Quadratic loss function, Hellinger and Kullback-Leibler loss function, especially in case of having volatility and time-varying parameters.