PurposeOne of the most important sources of energy in the world, due to its great impact on the global economy, is the crude oil. Due to the instability of oil prices which exhibit extreme fluctuations during periods of different times of market uncertainty, it became hard to the governments to predict accurately the prices of crude oil in order to build their financial budgets. Therefore, this study aims to analyse and model crude oil price using the hidden Markov process (HMM).Design/methodology/approachTraditional mathematical approaches of time series may be not give accurate results to measure and analyse the crude oil price, since the latter has an unstable and fluctuating nature, hence, its prediction forms a challenge task. A novel methodology that is so-called the HMM is proposed that takes into account the heterogeneity in prices as well as their hidden state-based behaviour.FindingsUsing the Bayesian approach, several estimated models with different ranks are fitted to a non-homogeneous data of Iraqi crude oil prices from January 2010 into December 2021. The model selection criteria and measures of the prediction performance of each model are applied to choose the best model. Movements of crude oil prices exhibit extreme fluctuations during periods of different times of market uncertainty. The processes of model estimation and the model selection were conducted in Python V.3.10, and it is available from the first author on request.Originality/valueUsing the Bayesian approach, several estimated models with different ranks are fitted to a non-homogeneous data of Iraqi crude oil prices from January 2010 to December 2021.