PREDICTING FUTURE PRICE OF CRUDE OIL (BONY LIGHT)

ByEric L. Otuonye*& Chigozie Okororie**

*Department of Statistics, Abia State University, Uturu, Nigeria **Department of Statistics, Imo State University, Owerri, Nigeria

* eric.otuonye@yahoo.comAbstractThe work examined the price of crude oil (Bony Light) from 2006 to 2013 using the descriptive approach to time series analysis. Buys-Ballot table was used to assess the stability of the variance of the data, choice of model and seasonal effect. The quadratic trend was found to be appropriate with appreciable seasonal effect. The month of April has the highest seasonal index while the month of October has the least index.

Keywords: Buys-ballot table, Data transformation, Periodic means and standard deviations, Choice of model, Trend assessment, Seasonal indices, Normality, Forecast.

1. Background of the studyLike prices of other commodities, the price of crude oil experiences wide price swings in times of shortage or oversupply. The crude oil price cycle may extend over several years responding to changes in demand as well as OPEC and non-OPEC supply. Throughout much of the twentieth century, the price of U.S. petroleum was heavily regulated through production or price controls. In the post-World War II era, U.S. oil prices at the wellhead averaged $28.52 per barrel adjusted for inflation to 2010 dollars. In the absence of price controls, the U.S. price would have tracked the world price averaging near $30.54. Over the same post war period, the median for the domestic and the adjusted world price of crude oil was $20.53 in 2010 prices. Adjusted for inflation, from 1947 to 2010 oil prices only exceeded $20.53 per barrel 50 percent of the time. Until March 28, 2000 when OPEC adopted the $22-$28 price band for the OPEC basket of crude, real oil prices only exceeded $30.00 per barrel in response to war or conflict in the Middle East. With limited spare production capacity, OPEC abandoned its price band in 2005 and was powerless to stem a surge in oil prices, which was reminiscent of the late 1970s.

Energy plays the central role in the world economy. In spite of considerable inclination to alternative renewable sources of energy like wind, water, nuclear and solar power, the role of crude oil in macroeconomic movements has not waned yet (Mehrara & Mohaghegh, 2011).

Since the discovery and production of oil Nigeria in 1958, the subsector has continued to play a major and dominant role in the Nigerian economy. The extractive sector in the Nigerian economy is large and extensive, with oil playing a vital role. With nearly 37.2 billion barrels in reserves and 2.13% of global production, Nigeria has the world’s tenth largest proven reserves (3.1% of global reserves), and is among the top 10 oil producers (Akinlo, 2012).

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Nigeria has been a member of the Organization of the Petroleum Exporting Countries (OPEC) since July 1971. Currently, there are 12 member countries including Nigeria in this international organization whose aim of the organization, according to its Statute, is the determination of the best means for safeguarding their interests, individually and collectively; devising ways and means of ensuring the stabilization of prices in international oil markets with a view to eliminating harmful and unnecessary fluctuations; giving due regard at all times to the interests of the producing nations and to the necessity of securing a steady income to the producing countries; an efficient, economic and regular supply of petroleum to consuming nations, and a fair return on their capital to those investing in the petroleum industry (OPEC, 2012).

Crude Oil is an important commodity not just because it is naturally occurring in the earth but because of the many fractions that are derived from it after the refining process. Those varying fractions such as fuel oil, jet fuel, kerosene etc. are extracted at different temperatures during the refining process.

The demand for crude oil is derived from the demand for its fractions and it depends on a large number of factors such as its grade, sulphur content and its locations. Crude Oil is classified in the international market according to varying molecular characteristics by giving pricing references to the areas where such barrels are produced. Such pricing references include the North American West Texas Intermediate, Nigerian Bonny Light, Brent etc.

Oil price is highly variable; even more than any other commodity. Crude oil prices have increased on average from US $25 per barrel in 2002 to US $55 per barrel in 2005. There has been a steep upward trend in the price of crude oil in recent years, reaching a record nominal high of US $147 in mid-2008 and a sharp drop to US $46 a barrel. The huge revenues from oil, of course, presented net wealth and thus provided opportunity for increased expenditure and investment; however, the huge revenues complicated macroeconomic management and also made the economy highly oil dependent. Asides, in spite of the huge rents from oil, the economy still grapples with many problems including high and rising unemployment rate, declining manufacturing production, high and rising level of poverty and poor infrastructural development. The dismal performance of the Nigerian economy in the face of huge rents from oil has rekindled interest on the importance of oil in the growth and development process in Nigeria.

In 1974, Michael Kennedy developed a regional multi-commodity optimization model of the world oil market. The model was a static model and had four sectors including crude production, transportation, refining and consumption. It also had seven trading regions and assumed a monopolist behavior for OPEC.

The model studied the consequences of OPEC’s behavior through simulating the effects of export taxes. The model results showed that the high prices in 1973 are not likely to remain as

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large producers will have problems allocating reduced production. Alsmiller and Horwedel (1985) developed a dynamic World Oil Market (WOM) model for the period 1980-2040 to be a part of the framework of another model, the Generalized Equilibrium Modeling System (GEMS) which is available from Decision Focus Incorporated. The GEMS system is basically a group of process sub-modules that are connected together and their equations are solved simultaneously to determine prices and quantities as functions of time. In the WOM, results were presented for two cases, when OPEC is treated as a Stackelberg cartel and when OPEC is treated as a competitive producer. Model results showed that full cooperation among OPEC member can cause a 25% increase in the oil price for 1990-2010. In 1986, Lorentsen and Roland developed a traditional simultaneous econometric model for the world oil market for the Norwegian Ministry for Oil and Energy. Their model was used to trace crude oil price throughout the year 2000. Several scenarios were developed for different economic growth and conservation rates and for different alternative energy prices. A year later, Geroski, Ulph, and Ulph (1987) developed an empirical model for the world oil market where the pricing conduct is allowed to respond to several factors and can vary over time. Changes and variation in players’ behavior appears to be playing an important role in price movements and tit-for-tat strategy (discipline and reward) was found consistent with the data.

To analyze oil market conditions and oil prices, Amano (1987) developed a small-scale econometric model for the oil market. The model simulation results anticipated wide price fluctuation if OPEC’s core members (Saudi, Kuwait, UAE, Qatar, Libya) attempt to defend the cartel’s market share. A year later, Baldwin and Prosser (1988) developed a recursive simulation model for the World Oil Market (WOM) and various strategies for OPEC were tested assuming that OPEC can set either the price or the output. Both oil consumers and non-OPEC producers were assumed to be price takers where consumers maximize their benefits and non-OPEC countries maximize their profits. OPEC on the other hand is assumed to set either price or quantity. Results showed that supply and demand could balance for a range of prices and OPEC output depending on what strategy OPEC adopts.

Another econometric model for the oil market was developed by Robert Kaufmann (1994) to integrate the effects of economics, geological, political and environmental changes. The model by Kaufmann forecasted oil prices based on market condition and OPEC behavioral changes. In fact, the model results showed that OPEC can influence medium and long run prices through the rate they add capacities.

The ultimate aim of this paper is to determine the trend pattern of crude oil price. While the specific objectives are:(1)The appropriate choice of the model to be adopted i.e. multipliative, additive or mixed model using Iwueze and Nworgu (2004).

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(2) The type of transformation to be adopted (if applicable) in the analysis of the data using Bartlett (1947) which was summarized by Iwueze and Akpanta (2009) and shown below in table 1. This could be regarded as a power function where

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Table 1: Transformation TableS/No 1 2 3 4 5 6 7

Values of β 0 1 2 3 -1

transformation No transformation LogeXt

(3) To determine the impact of seasonal effect on the observed series and the probability of forecasting future trend pattern.

2. MethodologyThe general time series is a mixture of four components (Kendal and Ord, 1990). The components are; (i) The trend or long term movement of the series. (ii) The seasonal component (iii) The cyclical component or fluctuations about the trend (iv) The irregular, random or error component.

The trend and cyclical components could be combined to give the trend-cycle component especially in short time series (Chatfield, 2004). Time series which is an ordered set of observations made sequentially in time has three main models which are used in descriptive time series analysis. They are the multiplicative, additive and the mixed models. The models are expressed mathematically as;

Multiplicative: 2

Additive: 3

Mixed: 4

Where Tt is the trend over time t, St is the seasonal variation over time t, Ct is the cyclical variation over time t, It is the irregular or error variation over time t and M t is the trend-cycle variation over time t when short period of time is observed, the cyclical component is superimposed into the trend component.

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In statistics, data transformations refer to the application of a deterministic mathematical function to each point in a data set. Data transformations are generally used in time series so that the data approximately meet the assumption of a statistical inference procedure that is to be applied to a collection of comparable measurements.

The criterion on how data should be transformed or whether transformation is applicable at all should emanate from the particular statistical analysis to be carried out.

Generally there are a number of reasons for data transformation like easy visualization, improvement in interpretation, variance stabilization, ensuring a normally distributed data, additivity of the seasonal effect. However, for time series data there are three major reasons namely; (1) Variance Stabilization transformation (2) Ensuring a normally distributed data (3) Additivity of the seasonal effect.

In this work, we would explore the appropriate transformation which would be adopted in the analysis of consumer price index of dairy in Nigeria to ensure that the data meet an appropriate inference procedure.

3. Analysis and DiscussionsTable 1: Collected data from CBN website (www.cenbank.org)

Year Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec2006 63.71 60.37 62.95 71.8 71.18 69.32 75.13 75.15 63.46 59.44 60.1 65.462007 55.57 59.97 58.47 70.46 70.4 73.39 79.62 73.9 79.81 83.73 95.05 93.42008 94.26 98.15 103.73 116.73 126.57 138.74 141.86 115.84 103.83 75.31 54.31 44.362009 44.95 46.52 49.7 51.16 60.02 72.24 66.52 74 70.22 78.25 78.11 75.112010 77.62 75.06 80.27 85.29 77.54 75.79 77.18 78.67 79.45 84.42 86.71 932011 97.96 106.57 116.56 124.49 118.43 117.03 117.86 111.99 115.73 113.12 113.92 111.462012 113.81 121.87 128 122.62 113.08 98.06 104.62 113.08 98.06 108.92 111.05 111.492013 115.24 118.81 112.79 105.55 106 106.06 109.78 107.84 113.59 112.29 111.14 112.75

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Fig. 1: Time plot of the original series.

(i) Choice of TransformationUsing Bartlett (1947) and the structured transformation guide, Iwueze and Nworgu (2004), figure 2 below shows the regression plot of the natural logarithm of the periodic mean and natural logarithm of the standard deviation.

Fig. 2: Fitted line plot of group log std against group log mean

The regression equation is

= 3.12 - 0.21

In other to determine the appropriate transformation, the periodic (annual) means and standard deviations only will be used. The slope of the regression equation of natural logarithm of the

standard deviations against the logarithm of the periodic means of the data was

found to be -0.21 with the standard error 0.2816 and coefficient of determination R2 = 0.421.

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Iwueze and Akpanta (2009:241) said that it is better to substitute the value of the slope directly in the power transformation derived (see equation 1). Substituting the value of β (-0.21) in equation 1 (the power function), the exact transformation for the data is

5Equation 5 represents the exact transformation to be carried out.

Fig. 3: Time plot of the exact transformation

(ii) Choice of appropriate model

Using Buys-Ballot table, the relationship between the periodic means and the

periodic standard deviations , where n is the number of years, gives an

indication of the desired model. An additive model is appropriate when the seasonal standard deviations show no appreciable increase/decrease relative to any increase or decrease in the seasonal means. On the other hand, a multiplicative model is usually appropriate when the seasonal standard deviations show appreciable increase/decrease relative to any increase/decrease in the seasonal means, Iwueze et al, 2011.

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Fig. 4: Time plot of group means and std deviations

From figure 4 above, the amplitude of both the seasonal and irregular variations changes as the level of the trend changes (the two plots are not moving in the same direction). This suggests that an additive model is most appropriate for the decomposition.

(iii) Trend Analysis By direct observation of the time plot, it suggests either a linear or curvilinear trend. There are guiding principles on how to determine the adequate trend model and pattern for a particular set of data. Comparing the errors (accuracy measures) committed in fitting the trend. In this work, accuracy measures adopted are the Mean Absolute Percentage Error (MAPE), Mean Absolute Deviation (MAD) and Mean Squared Deviations (MSD) of the fitted trend patterns.

Fig. 5: Linear trend analysis of the transformed data

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Fig. 6: Quadratic trend analysis of the transformed data.

Table 2 below shows the comparison of their respective accuracy measure and errors committed in fitting the trends

Table 1: Table of Accuracy Measures

Trend TypeAccuracy measures

MAPE MAD MSDLinear 21.13 42.70 3253.63Quadratic 20.98 42.80 3240.31

Clearly, the quadratic trend committed the least error is committed in the curve fitting. This implies that quadratic trend is the line of best fit. The estimated trend line is given byYt = 161.7 + 1.170 t + 0.00531t2; t = 1, 2, . . ., 96

Substituting successive values of t in the above equation, gives the values of the trend component, Mt.

The plot of the detrended data is shown figure 7 below.

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Fig. 7: Plot of the detrended series

(iv) Assessment of Seasonal Effect The methods available for analysis of seasonal time series data in the time domain approach include the descriptive method and the fitting of probability models (Box et al, 1994; Chatfield, 1980). Traditionally, seasonal effects determination in the descriptive method is not done without some prior adjustments for the trend. We must remember that the common values of s (seasonal length) for variation within a year are: s = 1 for yearly data; s = 2 for data collected two times a year; s = 3 for data collected three times in a year; s = 4 for quarterly data showing seasonal effects within years; s = 6 for bi-monthly and s = 12 for monthly data showing seasonal effects within years as outlined by Iwueze et al, 2008.

Table 2: Table for the Seasonal Indices S/n 1 2 3 4 5 6 7 8 9 10 11 12Month Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec

Index -6.51 -5.46 8.53 1.95 -0.21 0.75 1.15 4.25 -5.32

-12.4

-8.83

-7.87

The sum of the seasonal indices is zero conforms to Iwueze et al (2008).

(v) Estimation of the Error Component Traditionally for an additive model, estimation of error component involves subtracting other estimated components (trend-cycle and seasonal components) from the original or transformed series where applicable. Mathematically expressed as

6The plot of the error component is shown on figure 8 below.

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Fig. 8: Plot of the error series

(vi) Test for Normality Assumption One of the assumptions of time series analysis / Ordinary Least Squares (OLS) is that the error is random and normally distributed with mean 0 and some variance i.e. for an additive model. This assumption is very important in time series analysis because when met, the fitted model could be used in predicting (forecasting) future trend pattern.

Approximate P-Value: 0.044D+: 0.093 D-: 0.080 D : 0.093

Kolmogorov-Smirnov Normality Test

N: 96StDev: 56.4285Average: 0.0721979

2001000-100

.999

.99

.95

.80

.50

.20

.05

.01

.001

Prob

abili

ty

error

Normal Probability Plot

Since D-statistics 0.093 is less than = 118.1, we accept the hypothesis that the error component is random and the model is adequate for forecasting.

(vii) ForecastUsing the fitted trend (quadratic) model, forecast for 2014 was estimated and shown on table 5.

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Table 3: Forecast table for year 2014S/N Month Transformed Forecast

1 January 318.6452 February 321.8953 March 338.0984 April 353.7455 May 333.8286 June 337.0407 July 349.6948 August 345.0659 September 337.77710 October 332.948

S/N Month Transformed Forecast11 November 338.85512 December 342.129

ConclusionThis paper has examined the Crude Oil Price (Bonny Light) using the descriptive approach to time series analysis. Buys-Ballot approach was adopted in assessing the assumptions of time series analysis for valid inferences. The month of April showed the highest price index while November has the least price.

REFERENCES

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