THE RETAIL AND DISTRIBUTION GASOLINE MARKET IN BRAZIL-A STUDYOF VARIATION PRICE BEHAVIORS

In this paper evaluates the effects in the gasoline prices after the Brazilian downstream oil chain liberation, in late 1990s. That stage meant that the Brazilian govern, that no longer setting the maximum and minimum values of all fuels. For this purpose, the gasoline type C prices were collected from fifteen relevant cities in five economic regions of Brazil, between the years 2005 and 2014. The sequences of computational techniques were applied on these datasets. The stationary and linearity for variation prices time series were analyzed in all cities and, also, the correlations among all cities in order to recognize the times series patterns. Furthermore, the Cumulative Sum control (CUMSUM) chart was used to detect smaller parameter shifts on the distribution time series. Our results reveled distinct patterns for middle of 2005 and the middle of 2006, and also for the first months of 2011 and the middle of 2012. Reinforcing the idea of the Brazilian retail and distribution are governed strongly by exogenous factors. This makes a conventional analysis difficult to be used. Once, the Brazilian downstream fuel chain suggests to be a complexity system.


INTRODUCTION
After the oil control changing a new status quo was established in Brazil.
The Brazilian govern no longer setting the maximum and minimum values of fuel, their derivatives or any requirement of prior official authorization for price adjustments among others.The main aims were to improve the infrastructure industries, protect the competition and efficiency of market.For these purpose, it was created the Brazilian law 8884/94, called Petroleum law, which begun a new phase in Brazilian downstream oil chains.Three years after, the law 9.478 was published, it created the National Agency of Petroleum, Natural Gas and Biofuels (ANP), in order to regulate and supervise the petroleum industry, its derivatives, natural gas and biofuels in Brazil.Uchoa (2006) points out about the behavior of oil prices in international trade generate impacts on their derivatives from a global market.In Brazil, this phenomenon is not different.There, although with a low volume of petroleum imports, around 5% according to Petrobras (2005) and ANP (2016), the prices of their derivatives are not detached from the variations of the international oil market.So that changes in oil prices directly impact socioeconomics (e.g., freight cost, vehicle sales, and urban transport, among others).The Brazil has a larger car fleet, and the gasoline fuel has been the second most consumed fuel, that coming just behind the diesel oil.Hence, the gasoline has a straight impact on family budget.Furthermore, the Brazilian downstream fuel chain segment had been an easing of entrance since 1993 and according to ANP, in the year of 2013 there were 38,893 fuel retails, with the main distributions companies such as: BR, Ipiranga, Chevron, Shell, Esso and Alesat, where they have around 43% of the market share, and the rest of occupying with small retailers, called "white flags" (ANP, 2016).According Silva (2014) take account the structure of prices in the retail and distribution gasoline market in Brazil, it is important to note aspects of price construction and regional differences that make aggregate analysis less effective, for understanding the behavior of agents in the formation of prices.
Thus the differences among prices, fuel taxation practices undertaken by states, distances, and costs of fuel could be difficult to understanding the gasoline prices behavior.
The aim of this paper is to evaluate the stochastic process gasoline type C on retail and distribution market for fifteen cities in five economic regions in Brazil, between 2005 and 2014.For this purpose, it was suggested a sequence of steps to support this study, including a stationary and linearity test, a correlation analysis and Cumulative Sum (CUSUM) control chart processes, that is suitability to detect smaller parameter shifts in time series (TS).This work is structured as following: after this introduction, in the section two we can find materials and methods; third section presents the results and considerations are in the fourth section.

Data
In this paper it is evaluated the behavior of price of gasoline type C in fifteen cities in Brazil between 2005 and 2014 (see the Table 1).Where their data were collected from weekly survey of prices for retail and distribution where that is carried out in 555 municipalities.The service is provided monthly by ANP.

Time series evaluation
In general, there are situations where a researcher takes a looked at the dataset or graphs and rapidly it is chosen a TS analysis method.Sometimes without recognize how the dataset is governed.That may occur due the researcher to be an expert in specific tool, and believe that one could solve any kind of problems by applying the same tool.Thus, to avoid that situation, first of all, it is recommended the researcher to observe carefully the characteristics of the dataset under study.Thereby, before choosing the final method and to avoid a prejudice, here it is suggested three steps that may help, mainly, new researchers.

Procedures
Before applying nonlinear techniques, e.g., those inspired by chaos theory, in occurrences of phenomena of nature, it is first necessary to know whether the use of such advanced techniques is justified by the data (Schreiber, 2000).In the Figure 1 depicts the sequence of this suggested verification, composed by three steps as following:  (Dickey, 1979;Dickey, 1981)  Step 2 -To verify the linearity behavior.We suggest a surrogate data analysis test (e.g., Random Shuffle (Monte Carlo) or Fourier Transform (Schreiber, 2000)).

RESULTS
It was evaluated the TS of gasoline type C variation prices for fifteen cities in Brazil, between 2004 and 2015.Figure 2 depicts the dispersion behaviors of these cities.It might be observed an imbalanced dispersion in both markets.For instance, the cities SSA and FP presented large dispersion whereas DF and RB small one.
In the next subsection it is evaluated the datasets under the stationarity approaches.

Stationary evaluations
During assesses of these datasets by using the methodology in Figure 1, there were detected for all datasets a stationary behavior by busing ADF (Dick-Fuller) with lag − 1 (Dickey, 1979;Dickey, 1981).

Linear evaluations
Although the distribution dataset either retail analysis shown a stationary behavior some of those data presented non linearity.The Figure 3 depicts a surrogate data analysis for RJ, with H 0 rejected for this kind of test.Since there are cases of non-linear behaviors (see Table 2) is necessary to apply other techniques to better explain the dataset behaviors.In the next subsection we evaluate these TS with computational complex methods.

Application of Statistical Techniques
We shall use complex statistical techniques to evaluate these TS, because there are some non-linear series on the results found in Section 3.2.It will be presented two different statistical analyzes in this case study problem.

Spearman's rank correlation coefficient
The Spearman correlation evaluates the monotonic relationship between two variables.We calculated the spearman value to find for strong correlations for each distribution and retail variations series inside each city.The following equation is used to calculate the Spearman coefficient ρ: (1) Where: d i is the difference between the ranks of corresponding values X i and Y i , both are original TS and n is the number of value in each data set.

Source: author
We plotted the top four strongest spearman correlation results to evaluate the graph pattern (Figure 4).Rio de Janeiro weekly distribution variations are associated with retail weekly variations.k: The upper and lower CUSUMs essentially accumulate deviations from target that exceed a slack value.k is typically set to be equal to half of the distance from the target (µ 0 ) and the shifted mean (µ 1 ) that we want to detect (Eq.2). (2) We used h = 4 and k = 0.5 to evaluate this series.In addition, we defined the target as the historical mean for each city in the CUSUM Chart design (Figure 6).

FINAL CONSIDERATIONS
In this paper the variation prices of gasoline type C were evaluated for five economic regions in Brazil.It was followed a three steps methodology where they were underlying behavior by using a set of techniques.We tested the stationarity by using ADF (Dickey, 1979;Dickey, 1981) and linearity by using a surrogate data analysis (Schreiber, 2000).Besides, it was applied computational techniques such as Spearman correlation, regression dataset analysis and CUMSUM analysis (Montgomery, 2001) in order to evaluate the complexity of the datasets.Our finds reinforce the idea that of the Brazilian downstream fuel chain, retail and distribution are governed by complexities behavior.Thereby, conventional statistics could be not appropriate economics data.In this way we suggest, mainly for new researcher, follow the steps of this paper in order to conduct a research in complex field of science, as economics issues among others complex disciplines.

Figure 1 -
Figure 1-Strategy used to evaluate the time series behavior.

Figure 2 -
Figure 2-Boxplot shows two capitals with greater variation than any other city (SSA and FP), for both distribution (a) and retail (b) markets.

Figure 3 -
Figure 3-Surrogate data test analysis for RJ distribution time series.Where the solid black vertical line is the shuffled original time series by Monte Carlo simulation and the red dashed line is the discriminating statistic between both original data and the surrogate data.If the value of the statistic is significantly different for the original series than for the surrogate set.

Figure 4 -
Figure 4 -Scatterplot for top four strongest spearman correlation results.
In addition, we generated a Dotplot graph with every out of control point found on CUSUM chart, divided by year (Figure7).Dot plot is used to evaluate and compare distributions by plotting the values along a line and useful for comparing distributions.The x − axis for a Dotplot is divided in small intervals.Data values falling within each box are represented by dots.We can see many dots plotted for all cities in two different periods: first, between the middle of 2005 and the middle of 2006, and second, between first months of 2011 and the middle of 2012.According to Cadernos do CADE varejo de Gasolina (2014), Brazilian market had some acts of concentration between fuel distributors between 2000 and 2012.Specifically, in 2006 we had a fusion between Ale e Satelite groups, creating the Alesat.In 2012, Alesat acquire the Ello-Puma and Raízen acquire the Mime group.It could be a starting point to understand the found behavior in these series.

Table 1 -
Cities evaluated in every Brazilian regions.

Table 2 -
Cities that presented non-linear behaviors.

Table 3 -
Distribution versus Retail Spearman Correlation by Brazilian regions.