Gibbs Sampling Algorithm

Modeling of oil price behavior depends on whether we distinguish the observed data as examples of deterministic or random trend processes. The distinction between these processes is crucial because of the long-term response of data series to shocks. Generally, in standard significance tests, the null hypothesis is tested for the difference between the insignificant and significant hypotheses. In the present study, to investigate the root of the non-difference stationary unit from Bayesian methods, we estimate the RCAR model considered for oil prices. The results of this study show that despite confirming the unit root in oil price data, it is not clear that whether a random step process is suitable for predicting Brent crude oil prices or not because confirming the existence of a random unit root does not necessarily mean that the crude oil spot prices follow a Brownian process. Therefore, it is not possible to conclude from such results that the efficiency of the oil market is insignificant. However, because the unit root in the crude oil data is random, it does not persist with the differentiation of the crude oil data; therefore, the use of the differentiated variable in conventional co-integration models will be incorrect. Also, because the crude oil is the input of many industries, this anonymity could be transferred to other macroeconomic variables. Therefore, theories of business cycles that portray temporary economic shocks will have weak support.

The main drawback of classical ADF and PP tests is the low power of test in small samples and their asymptotic distribution discontinuous. In contrast, many prominent scholars support the Bayesian unit root tests. In the present study, Bayesian unit root tests as an alternative to the classical methods are investigated. Because of the unconditional distribution structure of financial data, the focus of this study is to adjust the likelihood function with the distribution of the Scale Mixture of Normal. Daily stock returns data of 50 active stock companies were used. Due to the high probability of outliers, the unit root test was performed in terms of outliers’ observations without the need to construct new test statistics. The simulation results with Gibbs sampling algorithm show high probability of stationery. Also, the simulation of the distribution of the unit root test parameter shows that the Bayesian approach is more accurate than the classical one.