Using SARFIMA and SARIMA Models to Study and Predict the Iraqi Oil Production

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1 2011, TextRoad Publication ISSN X Journal of Basic and Applied Scientific Research Using SARFIMA and SARIMA Models to Study and Predict the Iraqi Oil Production Hamidreza Mostafaei 1, Leila Sakhabakhsh *2 1 Department of Statistics, Tehran North Branch, Islamic Azad University, Tehran, Iran. & Department of Economics Energy, Institute for International Energy Studies (IIES), (Affiliated to Ministry of Petroleum) h_mostafaei@iau-tnb.ac.ir 2 MSc. Of Statistics, Islamic Azad University, North Tehran Branch, Tehran, Iran. ABSTRACT In this paper the specification of long memory has been studied using monthly data in oil production in Iraq in the period of (Jan 1997 to Mar 2010). Due to the US invasion to Iraq in 2003, its oil production decreased and this factor caused a sudden change in Iraqi oil production. Since the existence of a sudden change can lead to large prediction errors and uncertainty of the model, Iraqi oil production is investigated separately for two periods, before and after the US invasion. Actually, the whole data is divided into two sub-samples. Since in both sub-samples, monthly series of Iraqi oil production is showing non-stationary and periodic behavior, SARFIMA and SARIMA Models are fitted into the data; and their parameters are estimated making use of conditional sum of squares. The results show that there is no long memory in both sub-samples therefore dependency of the observations far from each other is insignificant; so the second sub-sample was used for prediction. The best model is SARIMA (0, 1, 0) (0, 0, 1) 12 which is used to predict the rate of oil production in Iraq till the end of JEL Classification: C13; C22; C53 KEY WORDS: Long memory; Conditional sum of squares; SARFIMA model; SARIMA model. INTRODUCTION Iraq holds a considerable portion of the world's conventional oil reserves, but due to the US invasion to Iraq in 2003, its oil production decreased and this factor caused a sudden change in Iraqi oil production. Therefore Iraq has been unable to increase oil production substantially in recent years due to conflict and geopolitical constraints. As violence in Iraq has lessened, there has been a concerted effort to increase the country's oil production, both to bolster government revenues and to support wider economic development. Recently, Iraq offered prequalified foreign oil companies two opportunities to bid on designated fields under specific terms of investment. The success of the bidding rounds and the level of interest from foreign companies have raised hopes that oil production could increase substantially over a short period of time, with some Iraqi government officials stating that the country could increase its production to 12 million barrels per day by 2017.Although Iraq has the reserves to support such growth, it will need to overcome numerous challenges in order to raise production to even a fraction of that goal. In this paper we intend to forecast Iraqi oil production in the future. In order to, we use SARIMA and SARFIMA models to construct an adequate model for Iraqi oil production. The recent finance and economic literature has recognized the importance of long memory in analyzing time series data. A long memory can be characterized by its autocorrelation function that decays at a hyperbolic rate. Such a decay rate is much slower than that of the time series, which has short memory. Traditional models describing short memory, such as AR (p), MA (q), ARMA (p, q), and ARIMA (p, d, q) cannot describe long memory precisely. A set of models has been established to overcome this difficulty, and the most famous one is the autoregressive fractionally integrated moving average (ARFIMA or ARFIMA (p, d, q) ) model. ARFIMA model was established by Granjer and Joyeux (1980). An overall review about long memory and ARFIMA model was model by Baillie (1996). In many practical applications researchers have found time series exhibiting both long memory and cyclical behavior. For instance, this phenomenon occurs in revenues series, inflation rates, monetary aggregates, and gross national product series. Consequently, several statistical methodologies have proposed to model this type of data including the Gegenbauer autoregressive moving average processes (GARMA), k-factor GARMA processes, and seasonal autoregressive fractionally integrated moving average (SARFIMA) models. The GARMA model was first suggested by Hosking (1981) and later studied by Gray et al (1989) and Chung (1996). Other extension of the GARMA process is the k-factor GARMA models proposed by *Corresponding Author: Leila Sakhabakhsh, MSc. Of Statistics, Islamic Azad University, North Tehran Branch, Tehran, Iran. Fax , leila.sakhabakhsh@yahoo.com 1715

2 Mostafaei and Sakhabakhsh, 2011 Giratis and Leipus (1995) and Woodward et al (1998). This paper investigates a special case of the k-factor GARMA model, which is considered by Porter Hudak (1990) and naturally extends the seasonally integrated autoregressive moving average (SARIMA) model of Box and Jenkins (1976). There are several methods for estimating the parameters in time series models. In this paper, we estimate the parameters using conditional sum of squares (CSS) method. MATERIALS AND METHODS ARFIMA model Let {ε } Z be a white noise process with zero mean and variance σ > 0, and B the backward-shift operator, i.e., B (X ) = X. If {X } Z is a linear process satisfying Φ(B)(1 B) X = Θ(B)ε, Z. (1) Where d (-0.5, 0.5), Φ(. ), Θ(. ) are polynomials of degree p and q, respectively, given by Φ(B) = 1 φ B φ B, Θ(B) = 1 θ B θ B Where φ, 1 i p, θ, 1 j q, are real constants, than {X } Z is called general fractional differentiation ARFIMA (p, d, q) process, where d is the degree or fractional differentiation parameter. If d (- 0.5;0.5), then {X } Z is a stationary, and an invertible process. The most important characteristic of an ARFIMA (p, d, q) process is the property of long dependence, when d (0.0; 0.5), short dependence, when d=0, and intermediate dependence, when d (-0.5; 0.0). SARFIMA (p, d, q) (P, D, Q) s processes In many practical situation time series exhibit a periodic pattern. We shall consider the SARFIMA (p, d, q) (P, D, Q) s process, which is an extension of the ARFIMA process. The following subsection presents some definitions and properties of these processes. Some definitions and properties Definition 1. Let {X } Z be a stationary stochastic process with spectral density function f (. ).suppose there exists a real number b (0, 1), a constant C > 0 and one frequency G [0, π] (or a finite number of frequencies ) such that f (ω)~c ω G, when ω G. Then, {X } Z is a long memory process. Remark 1. In Definition 1, when b ( 1, 0), we say that the process {X } Z has the intermediate dependence property. We refer Doukhan et al. [7] for more details. Definition 2. Let {X } Z be a stochastic process given by the expression φ(l)φ(l )(1 L) (1 L ) (x μ) = θ(l)θ(l )ε, for t Z, (2) Where μ is the mean of the process, {ε } Z is a white noise process with zero mean and variance σ ε = E(ε ), s N is the seasonal period, L is the backward-shift operator, that is L (X ) = X, = (1 L ) is the seasonal difference operator, ϕ(. ), θ(. ), Φ(. ), and Θ(. ) are the polynomials of degrees p, q, P, and Q, respectively, defined by ϕ(l) = ( ϕ )L, θ(l) = ( θ )L, Φ(L) = ( Φ )L, Θ(L) = ( Θ )L, (3) Where, φ, 1 i p, θ, 1 j q, Φ, 1 k P, and Θ, 1 l Q are constants and φ = Φ = 1 = θ = Θ. Then, {X } Z is a seasonal fractionally integrated ARMA process with period s, denoted by SARFIMA (p, d, q) (P, D, Q) s, where d and D are, respectively, the differencing and the seasonal differencing parameters. Theorem 1. Let {X } Z be a SARFIMA (p, d, q) (P, D, Q) s process given by the expression (3), with zero mean and seasonal period s N. Suppose φ(z)φ(z ) = 0 and θ(z)θ(z ) = 0 have no common zeroes. Then, the following is true. (i) The process {X } Z is stationary if d + D < 0.5, D < 0.5 and φ(z)φ(z ) 0, for z 1. (ii) The stationary process {X } Z has a long memory property if 0 < d + D < 0.5, 0 < D < 0.5 and φ(z)φ(z ) 0, for z 1. (iii) The stationary process {X } Z has an intermediate memory property if -0.5 < d + D < 0, -0.5 < D < 0 and φ(z)φ(z ) 0, for z 1. [2] CSS method There are several methods for estimating the parameters in time series models. In this paper, we implement the CSS method to estimate the SARIMA and SARFIMA models of oil production in Iraq. This method is equivalent to the full Maximum Likelihood Estimator (MLE) under quite general conditional homoskedastic distributions. A description of the properties of the CSS estimator and its finite sample performance is presented in Chung and Baillie (1993). 1716

3 The data The data employed in this study are the monthly data in oil production in Iraq in the period of (Jan 1997 to Mar 2010). The data are obtained from the Energy Information Administration of the U.S. Department of Energy. Figure 1 displays the data of oil production in Iraq, {x }. Sometimes events such as natural disasters, war, etc caused a sudden change in time series. Due to the US invasion to Iraq in 2003, its oil production decreased and this factor caused a sudden change in Iraqi oil production that it also is clear in Fig 1. (unit: Thousand Barrels Per Day) Fig 1. plot of oil production in Iraq (Jan 1997 to Mar 2010) Fig 2. The of monthly data of Iraqi oil production (Jan1997 to Mar2010) Partial Fig 3.. The P of monthly data of Iraqi oil production (Jan1997 to Mar2010) 1717

4 Mostafaei and Sakhabakhsh, 2011 As seen in figure 2, the slow decay in the autocorrelation function indicates the presence non-stationary in this time series. As mentioned earlier, due to the US invasion to Iraq in 2003, its oil production decreased and these descending trend continues to five months after the invasion. But after this period the rate of oil production approaches the amount produced before the invasion. Since the existence of a sudden change can lead to large prediction errors and uncertainty of the model, we omit these 5 data (Mar 2003 to Jul 2003). Then the whole data divide into two sub-samples. First sub-sample contains monthly oil production in Iraq in the period of (Jan 1997 to Feb 2003). Second sub-sample contains monthly oil production in Iraq in the period of (Aug 2003 to Mar 2010). Therefore Iraqi oil production is investigated separately for two periods, before and after the US invasion Fig 4. plot of oil production in Iraq (Jan 1997 to Feb 2003) Fig 5. The of monthly data of Iraqi oil production (Jan 1997 to Feb 2003) Fig 6. plot of oil production in Iraq (Aug 2003 to Mar 2010) 1718

5 Fig 7. The of monthly data of Iraqi oil production (Aug 2003 to Mar 2010) Figures 4, 5, 6, and 7 exhibit cyclical behavior. Since data are monthly, we consider s=12. As seen in figures 5 and 7, the slow decay in the autocorrelation function indicates the presence non-stationary in oil production series. In order to achieve stationary, these time series will need to be differenced. The plots of differenced time series are shown in Fig 8, 9. These plots show stationary Fig 8. plot of differenced data of Iraqi oil production (Jan 1997 to Feb 2003) Fig 9. plot of differenced data of Iraqi oil production (Aug 2003 to Mar 2010) Figures 10 and 11 display the of the differenced time series that these time series don't require seasonal differencing. Therefore the best transform for both sub-samples are y = (1 B)x. 1719

6 Mostafaei and Sakhabakhsh, 2011 Fig 10. The of differenced data of Iraqi oil production (Jan 1997 to Feb 2003) Fig 11. The of differenced data of Iraqi oil production (Aug 2003 to Mar 2010) Model selection To search for the best representation of this data, we first fitted differenced data y = (1 B)x by the CSS method, where we used a sample mean of {y }, y as an estimator of E[y ] = μ, and set s = 12. AIC and BIC criteria are also used under the assumption of normality [see, e.g., Brockwell and Davis (1991, section 9.3)]. Calculations of AIC and BIC are given by 2S(δ, σ ) + 2(number of estimated parameters) and 2S(δ, σ )+ log (sample size used for CSS estimation) (number of estimated parameters), respectively. Fitting SARFIMA models or SARIMA models is limited to having SARMA parameters with 0 p, q, P, Q 3, and where the total number of estimated SARFIMA parameters (d, D, SARMA parameters, and σ ) is less than 4. The total number of models is 70. As mentioned earlier, in addition to SARIMA models, SARFIMA models are fitted as well, because we intend to determine if the Iraqi oil production have long memory. From among these estimation results, we selected models in terms of AIC and BIC. All calculations were made using S-PLUS. Tables 1, 2 show the best five models in terms of AIC model selection with estimators. ID denotes the model identification within 70 models. indicates the corresponding parameter is not estimated and is set to be 0. The numbers in parentheses in the column of AIC (BIC) denote the ranking of models in terms of AIC (BIC). Table 1. Summary of AIC and BIC model selection estimates (first sub-sample) ID AIC BIC d D (1) (2) (3) (4) (5) (1)1044 (2)1044 (3) (4) (5)

7 Table 2. Summary of AIC and BIC model selection estimates (second sub-sample) ID AIC BIC d D (1) (2) (3) (4) (5) (1) (2) (4) (5) (3) In first sub-sample, SARMA (0, 2) (1, 0) 12 model (model ID: 16) is the best model in terms of AIC among the 70 model candidates. The best model for y is SARMA (0, 2) (1, 0) 12 model therefore the best model for x is SARIMA (0, 1, 2) (1, 0, 0) 12 model. In second sub-sample, SARMA (0, 0) (0, 1) 12 model (model ID: 21) is the best model in terms of AIC among the 70 model candidates. The best model for y is SARMA (0, 0) (0, 1) 12 model therefore the best model for x is SARIMA (0, 1, 0) (0, 0, 1) 12 model. When long memory does not exist in time series, dependency of the observation far from each other is insignificant. Therefore we use second sub-sample for predicting the rate of Iraqi oil production in the future. RESULTS AND DISCUSSIONS Forecasting The best model is SARIMA (0, 1, 0) (0, 0, 1) 12 model which is used to predict the oil production in Iraq till the end of 2012 and 2020, as shown in Fig 12, 13. Tables 3, 4 show the results of the In-sample and outsample forecasts for the SARIMA model Fig 12. Prediction plot of oil production in Iraq (Mar 2010 to Dec 2012) Table 3. Out-sample forecasts for the SARIMA (0, 1, 0) (0, 0, 1) 12 model Date Prediction lowercl lowercl: lower confidence limits of forecasts. uppercl: upper confidence limits of forecasts. uppercl

8 Mostafaei and Sakhabakhsh, Fig 13. Prediction plot of oil production in Iraq (Mar 2010 to Dec 2020) Table 4. In-sample forecasts for the SARIMA (0, 1, 0) (0, 0, 1) 12 model Date Actual Forecasts Error As seen in figures 12 and 13, Iraqi oil production has increasing trend for the future. In this paper, Iraqi oil production has been analyzed using previous years data but Iraqi oil production depends to other factors such as technology, politics, and security. The following also discuss the International Energy Outlook 2010 (IEO2010) report. In the IEO2010 Reference case, Iraq has an estimated 115 billion barrels of proven conventional oil reserves, the third largest in the world after Saudi Arabia (260 billion barrels) and Iran (138 billion barrels). However, Iraqi oil production was significantly affected not only by the U.S.-led invasion in 2003 and subsequent armed conflict, but also by neglect of the oil industry infrastructure and restrictions on investment resulting from United Nations sanctions imposed during the Saddam Hussein regime before the invasion. Oil production capacity has not increased substantially since the recent abatement of hostilities, and Iraq's current total production is about 2.5 million barrels per day still below the peak annual average of 2.9 million barrels per day in Between June 2009 and January 2010, Iraq awarded development service contracts for 10 oil projects to foreign companies, the majority of which were consortia formed to share the responsibility, risk, and, ultimately, returns on each of the projects. Originally, the Iraqi Ministry of Oil had expected the development of the fields up for bidding to raise Iraq's production capacity to 6 million barrels per day, in line with the Ministry's strategic goal. However, heavy competition and high expectations for the fields led bidding companies to propose production levels that were significantly higher than expected. As a result, rather than raising the country's total production to 6 million barrels per day, the proposed production from all awarded fields suggests that Iraq's total production could increase to 12 million barrels per day in EIA analysis suggests that, even in a stable political and security climate, it would be extremely difficult to raise production by nearly 10 million barrels per day over such a short period. The proposed pace and scale of Iraq's planned production expansion defy historical precedents and ignore a long list of logistical and political impediments. The uncertainty associated with the evolution of Iraq's upstream oil sector is reflected in the range of projections for liquids production in In the Reference case, the political and security situation in Iraq stabilizes, and a few of the operating companies overcome, in some measure, the obstacles they face. In this case, Iraq's total liquids production rises to 2.8 million barrels per day in 2017 and 6.1 million barrels per day in In the IEO2010 Low Oil Price case, Iraq's total liquids production reaches 8.3 million barrels per day by 1722

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