Test for Aggregational Gaussianity (AG) in Petroleum Prices Returns

The work aims at investigating and establishing if Aggregational Gaussianity, (AG) is in the dynamics of petroleum prices. This AG aspect is the phenomenon in which the empirical distribution of log-returns tends to normality (or as the time scale over which the returns are calculated increases). In order to achieve this, the petroleum price series was tested for arch effects. In addition, tests for Aggregational Gaussianity, (AG) were carried out using qualitative (graphical) approach and inferential approach, (involving statistical inference). The study shows that the presence of arch effects does not guarantee existence of AG. It is also observed that qualitative (graphical) approach may suggest normality and hence, presence of AG, on the other hand, inferential approach (involving statistical tests) gives a better picture of the actual conclusion, of the presence (or otherwise) of AG in the data set, with a 99.97% rejection from normality by the three tests-Kolmogorov-simonorv,Shapiro-Wilks, and Anderson-darling. In the circumstance, there is no evidence to confirm a discernible presence of AG in the dynamics of petroleum prices. The non-existence of AG in the study shows the instability in the dynamics of petroleum prices, since one cannot invoke normality as an invariant property this, among other factors, make the economy unstable as it is oil- driven. However, since the highest percentage of the budget for the country is based on the petroleum sales, which as this study reveals is unstable, hence, diversification of the economy is proposed. The softwares used in the work are Eviews 10, Minitab 18, Spss 17, Easy-fit 5.6 professional, and R 3.2.2.