European Journal of Scientific Research ISSN 1450-216X Vol.58 No.1 (2011), pp.30-37 © EuroJournals Publishing, Inc. 2011 http://www.eurojournals.com/ejsr.htm

Forecasting Electricity Generation in Nigeria using

Univariate Time Series Models

S. O. Adams Corresponding Author, Department of Statistics, University of Abuja, Abuja, Nigeria

E-mail: adamsamuel22003@yahoo.com

R. O. Akano Department of Statistics, University of Abuja, Abuja, Nigeria

O. J. Asemota

Department of Economic Engineering, Kyushu University, Fukuoka, Japan

Abstract

This paper fit a univariate time series model to the average amount of electricity generated in Nigeria between 1970 and 2009 and provides ten years forecast for the expected electricity generation in Nigeria. The Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) models are estimated and the best fitting ARIMA model is used to obtain the post-sample forecasts. The fitted model was ARIMA (3,2,1),with the Normalized Bayesian Information Criteria (BIC) of 13.906, stationary R2 = 0.69 and Maximum likelihood estimate of 411.55. The model was further validated by Ljung-Box test (Q14 = 6.404 and p>.10) with no significant autocorrelation between residuals at different lag times. Finally, ten years forecast was made, which showed a pick in the average electricity generation with estimated value as 3088.22 in the year 2011. Keywords: ARIMA, Autocorrelation, Partial autocorrelation, Serial dependence, Ljung-

Box-Pierce, PHCN. 1. Introduction Electricity generation is one of the seven point agenda of the present Nigeria government. Electric power industry in many countries all over the world is moving from a centralized operational approach to a competitive one, Nogales and Contreras (2002). In 2010, the Nigerian government took a bold step in greater involvement of the private sector in power generation in Nigeria. The Nigerian power sector operates well below its estimated capacity, with power outages being a frequent occurrence. In 2003, total installed electricity capacity was 5.9 gigawatts(GW), while total consumption was 14.5 Bkwh. According to Power Holding Company of Nigeria (PHCN), the electric demand in February 2006 was 7,600 megawatts (MW), but actual generation capability was 3,600 MW. The discrepancy between electricity demand and actual generation is mostly due to low water levels and inadequate plant maintenance. During year 2005, electricity generation capacity fluctuated between 2,600 MW and 3,600 MW. The electricity generated by hydropower stations at Kainji, Jebba, and Shiroro has been bedeviled by insufficient water. The Lagos Egbin, Delta, and Port Harcourt Afam plants are also operating at below capacity due to poor maintenance.

Forecasting Electricity Generation in Nigeria using Univariate Time Series Models 31

Only 40% of Nigerians have access to electricity, the majority of who are concentrated in urban areas. Despite endemic blackouts, customers are billed for services not rendered, partially explaining Nigeria's widespread vandalism, power theft and PHCN's problems with payment inadequacy. Some industries have collapsed due to the epileptic power supply in the country, Nigeria’s Bureau of Public Enterprises (BPE) hopes to see increased stability in Nigeria’s electricity sector once the ongoing privatization of PHCN fully takes effective.

Despite the importance of Electricity generation to the Nigerian economy, the literature is yet still scanty with published articles on Nigeria Electricity generation. This paper seeks to provide an appropriate ARIMA model to the data on electricity generation in Nigeria from 1970 - 2009. We choose this methodology because there is little or no research on electricity generation in Nigeria using the Box Jenkins analysis (see section 2). ARIMA model is used because of its generality; it can handle many series regardless of stationarity or not, with seasonal or without seasonal elements. The principle of parsimony of ARIMA model is also taken into consideration. The rest of the paper is structured as follows; section 2 presents the modeling and methodology, empirical results are presented in section 3, section 4 dealt with forecasting with the fitted model. The last section discussed the results obtained and suggested some recommendations. 2. Methodology 2.1. Model Specification

The model used in this study is the ARIMA proposed by Box and Jenkins (1976). The preliminary test for stationarity and seasonality of the data was conducted in which differences (d) as well as natural log were taken. After the stationarity of the series was attained, ACF and PACF of the stationary series are employed to select the order p and q of the ARIMA model. At this stage, different candidates’ model manifested and their parameters are estimated using the maximum likelihood method. Based on the principle of parsimony and model diagnostic tests, we obtained the best fitting ARIMA model. 2.2. Source of Data

The data used in this research work was extracted from the Central Bank of Nigeria statistical bulletin (December, 2007) and materials from Power holding Company Nigeria (PHCN). We obtained data on electricity power generation in Nigeria (1970 – 2009). The choice of this range is due to availability of the data from the source. 2.3. Method of Estimation: ARIMA Methodology

The Box-Jenkins model building techniques consists of the following four steps: Step 1: Preliminary Transformation: If the data display characteristics violating the

stationarity assumption, then it may be necessary to make a transformation so as to produce a series compatible with the assumption of stationarity. After appropriate transformation, if the sample autocorrelation function appears to be nonstationary, differencing may be carried out.

Step 2: Identification: If ty is the stationary series obtained in step 1, the problem at the

identification stage is to find the most satisfactory ARMA (p,q) model to represent ty . Box - Jenkins

(1976) determined the integer parameters (p,q) that govern the underlying process ty by examining

the autocorrelations function (ACF) and partial autocorrelations (PACF) of the stationary series, ty . This step is not without some difficulties and involves a lot of subjectivity. It does on occasion happen that evidence examined at this stage may not point clearly in the direction of a single model (Salau, 1998). Hence, it is useful to entertain more than one structure for further analysis. Salau (1998) stated that this decision can be justified on the ground that the objective of the identification phase is not to

32 S. O. Adams, R. O. Akano and O. J. Asemota

rigidly select a single correct model but to narrow down the choice of possible models that will then be subjected to further examination.

Step 3: Estimation of the model: This deals with estimation of the tentative ARIMA model identified in step 2. The estimation of the model parameters can be done by the conditional least squares and maximum likelihood.

Step 4: Diagnostic checking: Having chosen a particular ARIMA model, and having estimated its parameters, the adequacy of the model is checked by analyzing the residuals. If the residuals are white noise; we accept the model, else we go to step 1 again and start over. 3. Empirical Result In this section the ARIMA modeling strategy discussed in section 2.3 is applied to analyze the average electricity generation data. In this framework, model building commences with the examination of the plot of the series, the second logged difference plot, the sample plot of the autocorrelations (ACF), Partial autocorrelations (PACF), model description and forecast value using the fitted model. As in the first step of the Box- Jenkins, we tested for stationary in the data on the average electricity generation in Nigeria (1970 – 2009), (see fig1). An examination of Fig 1 clearly revealed that non stationarity is inherent in the data, after second differencing and taking Natural logarithm of the series, (see fig 2), we observed that the data on the chart was stationary. From a close observation of the ACF and PACF of the second logged differenced series, we noticed that the ACF cuts off at lag 1 but with significant spikes at lags 4. For the PACF plot, it is observed that it cuts of at lags 1 and 3 with a significant spike at lag 2. This implies that the stochastic process that generated the second logged differenced of the average electricity generated data is an ARMA model which has at most an MA (3) component. Hence, a number of possible models manifest themselves, these are ARMA (1,||1,2,3), ARMA (3,||1,2,3). i.e., ARIMA(1,2,1), ARIMA(1,2,2), ARIMA(1,2,3), ARIMA(3,2,1), ARIMA(3,2,2) and ARIMA(3,2,3). We proceeded to further statistical analysis with the six possible models. We summarized the results in Table 1.

Figure 1: Time Series plot of Electricity generated in Nigeria, (1970 – 2009)

Forecasting Electricity Generation in Nigeria using Univariate Time Series Models 33

Figure 2: Time Series plot of Second Logged difference

Figure 3: ACF of the second logged difference of Electricity generated in Nigeria

Figure 4: PACF for second logged difference of Electricity generation in Nigeria

34 S. O. Adams, R. O. Akano and O. J. Asemota

Table 1: Model Description

ARIMA STRUCTURE

Parameter Estimate

P - Value Stationary

R2 Likelihood &

BIC

Standard Error of estimate

Q- Statistics

1. ARIMA (1,2,1) AR{1} = -0.194 MA{1} = 0.998

0.324 0.852

0.58 371.183

BIC =13.971 0.193 5.310

12.763(0.690)

2. ARIMA(1,2,2) AR{1} = -0.997 MA{1} = -0.085 MA{2} = 0.881

0.000‡ 0.835 0.032†

0.50 277.182

BIC = 14.267

0.117 0.406 0.393

8.911(0.882)

3. ARIMA (1,2,3)

AR{1} = -1.00 MA{1} =-0.083 MA{2} = 0.853 MA{3} =-0.052

0.000‡ 0.835 0.013† 0.800

0.51 401.204

BIC =14.267

0.046 0.393 0.325 0.203

9.580(0.792)

4. ARIMA (3,2,1)

AR{1} =-0.478 AR{2} = -0.504 AR{3} = -0.370 MA{1} = 0.985

0.017† 0.017† 0.063† 0.094†

0.69 411.555

BIC = 13.906

0.189 0.200 0.192 0.520

6.404(0.955)

5. ARIMA(3,2,2)

AR{1} =-0.686 AR{2} = -0.580 AR{3} = -0.446 MA{1} = 0.753 MA{2} = 0.246

0.150 0.024† 0.045† 0.974 0.967

0.68 275.8

BIC = 14.037

0.464 0.244 0.214 23.157 5.929

6.352(0.932)

6. ARIMA(3,2,3)

AR{1} =-0.580 AR{2} = -0.889 AR{3} = -0.472 MA{1} = 0.803 MA{2} = -0.315 MA{3} = 0.509

0.196 0.016† 0.038† 0.869 0.777 0.847

0.67 275.302

BIC = 14.143

0.438 0.349 0.217 4.829 1.104 2.614

1.595(.998)

Notes: ‡ and † denote significant at the 1% and 10% levels respectively. Figures in parenthesis also denote P-values.

From Table 1, ARIMA structure 4 seems to be the most competitive model. The parameter estimates are all significant, the value of its stationary R2 is the highest and the Q statistics are also insignificant. The most important summary statistics for measure of goodness of fit are the R2, likelihood function (for maximum likelihood estimation), standard error of estimate and the Q statistic. For a well fitted model, the Q statistic is expected to be statistically insignificant. Another important criterion for checking the adequacy of a fitted model is the Normalized Bayesian Information Criteria (BIC). When considering several ARMA models, we choose the one with the lowest BIC. Based on these four important statistics and BIC, ARIMA structure 4 i.e. ARIMA (3,2,1) seems to provide the best satisfactory fit to the second logged differenced electricity generation series. This model has the highest likelihood function and the smallest standard error of estimate among all the ARIMA structures considered. Besides, the Q statistics is statistically insignificant suggesting that the residuals do not suffer from autocorrelation. 4. Forecasting with the Fitted Models In time series modeling researchers are motivated by the desire to produce a forecast with minimum error as possible. In this section, we assess the forecasting performance of Box-Jenkins models. The traditional Box-Jenkins approach is general and can handle effectively many series encounter in reality. Besides, previous research has demonstrated that the Box-Jenkins forecast out performs the Holt-Winters and stepwise auto regression forecasts, (Newbold and Granger, 1974). In addition, Naylor, T.H. et al. (1972) also showed the Box-Jenkins method give better forecasts than traditional econometric methods. Forecast from ARIMA model can be computed directly from the ARIMA model

equation by replacing, (1) future values of the error term by zero (2) future values of the ty by their

Forecasting Electricity Generation in Nigeria using Univariate Time Series Models 35

conditional expectation (3) present and past values of ty and t by their observed values. For example, the ARIMA (1,1,1) model ;

11)21(1 tεθtεtyty φtyty, may be written as

11211 )(1 tt-t-tt εθεφy y φ y has MMSE forecast at time N computed as;

3)2(ˆ)1(ˆ)1(

2)1(ˆ)1(

1)1(

)(ˆ

11

11

1111

NN

NN

NNN

N

yy

yy

yy

y

Where use is made of the parameter estimates of 11ˆ,ˆ and the observed residual N , see

(Chatfield, 2000) for more detailed discussions. By applications of the procedures discussed above, we computed one-step ahead forecasts for the fitted mode, i.e. ARIMA (3,2,1). These forecasts and their 95% confidence interval i.e. Lower confidence limit (LCL) and upper confident limit (ULC) for 10 years (i.e. 2010 – 2019) are summarized in Table 2, while Figure 5 depicts the observed and forecast plots of electricity generation in Nigeria. Table 2: Forecasted values with the Fitted Models

YEARS LCL FORECAST UCL 2010 1451.55 2423.91 3825 2011 1711.87 3088.22 5175 2012 1548.03 2847.73 4843 2013 1230.00 2308.77 3987 2014 1171.22 2387.21 4381 2015 1206.43 2629.10 5061 2016 1144.15 2591.98 5127 2017 1012.28 2373.3 4807 2018 937.91 2314.77 4854 2019 905.74 2358.66 5125

Figure 5: The plot of the observed and forecast value of Electricity generation in Nigeria

36 S. O. Adams, R. O. Akano and O. J. Asemota

The result presented above indicates that the average electricity generation in Nigeria will decrease in the long run, expect for the year 2011, where a slight increment is noticed. 5. Conclusions and Recommendations The epileptic nature of electricity generation in Nigeria has become unbearable to most Nigerians, especially in the big cities. It has posed a constant threat to the growth of the country’s economy. Furthermore, the present leadership as well as the incoming Government needs to take the issue of electricity generations seriously.

Forecasting the amount in megawatt the electricity generation can help the Government to take effective measure to handle any unexpected situation. This study is among the few in Nigeria on this area.

The paper examined the appropriate model that fits the aggregate electricity generated in Nigeria between 1970 and 2009. It was discovered that ARIMA (3,2,1) is the most suitable model for the series with the Normalized Bayesian Information Criteria (BIC) of 13.906, stationary R2 = 0.69 and Maximum likelihood estimate of 411.55 and the Ljung-Box test (Q14 = 6.404 and p>.10) was also estimated. The ARIMA model revealed that the average electricity generation in Nigeria will reduce further, with only a slight increment of about 3088.22 megawatt this year, (i.e. 2011).

Although a little increment is forecasted, in year 2011, the predicted megawatt is still not adequate for a population of over 150 million.

We therefore recommend that Government should as a matter of urgency hasten the privatization process so that more electricity can be generated given the available numerous natural resources in the country.

To date, there is no agreement on the actual figure expended in the energy sector from 1999 to 2007 this in itself is very worrisome, in the meantime, we urge the National Assembly to step up its oversight functions so as to find answers to the whereabouts of the $16 billion that the last administration claimed to have invested in the power sector and move the nation forward by ensuring that recent promises by the current administration remain a marked difference from previously failed promises. References [1] Asemota, O.J. (2010). “Modelling Nigeria’s crude oil Exports: State Space versus ARIMA

model”, Manuscript Submitted for Publication. [2] Ayodele A.S. (1998) “Energy Crises in Nigeria: The Case of Electric Energy” Market in

Bullion, 22 (4), pp. 19-23 [3] Brockwell, P.J. and Davis, R.A. (1996) (Introduction to Time series and forecasting” Springer,

New York. Section 3.3 and 8.3 [4] Central Bank of Nigeria (2008) Statistical Bulletin, 14(2) [5] Central Bank of Nigeria (1999), Annual Report and Statement of Account. Dec, pp 57 - 58,

129.Nigeria. [6] Chatfield, C. (2000). Time-Series Forecasting, Chapman & Hall/ CRC. [7] Dickey, D.A. and Fuller, W.A. (1981) “Likelihood Ratio Statistics for Autoregressive Process”.

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Forecasting Electricity Generation in Nigeria using Univariate Time Series Models 37

[11] Harvey, A.C.(1993) Time Series Models, 2nd Edition, Harvester Wheatsheaf, sections 3.3 and 4.4.

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