Study of the processes of evolution of prices for high-quality oil on international commodity markets based on the methods of modern mathematical statistics

The Russian economy depends on crude oil prices, and this study examines their fluctuations. Its objective is to investigate whether they can be described by the first-order Markov chain model. The analysis focuses on the historical prices of Brent Crude, the key crude oil benchmark, over the twelve months leading up to February 2024. A number of statistical tests are included in this study. First, a series of chi-square independence tests are conducted to uncover potential periodic patterns in price fluctuations. Second, a chi-square homogeneity test is used to determine whether the transition probabilities do not change with time. Third, a chi-square memory test is conducted to examine whether the price depends on the price two trading days earlier for a fixed price one trading day ago. The author's personal contributions include conducting a literature review, adopting and implementing statistical methods using Python, and analyzing the results. The main finding is that for moderate price discretization steps (e.g., 20 price intervals), the first-order Markov chain model assumptions cannot be statistically rejected at any reasonable significance level. However, for finer discretization steps (e.g., 40 price intervals), the data indicate the presence of memory (p-value = 0.014). The study's significance lies in showing that, depending on the price discretization step, the first-order Markov chain model should be used with caution and may require upgrading to a higher-order Markov chain model. The thesis comprises 74 pages, includes 14 figures, and cites 17 references.