Short-run electricity demand forecasts in Maharashtra

Applied Economics, 2002, 34, 1055±1059 Short-run electricity demand forecasts in Maharashtra SAJAL GHO SH* and AN JAN A D AS Indira Gandhi Institute of Development Research, Mumbai, India This paper, has tried to forecast monthly maximum electricity demand for the state Maharashtra, India, using Multiplicative Seasonal Autoregressive Integrated Moving Average (MSARIMA) method for seasonally unadjusted monthly data spanning from April 1980 to June 1999. The forecasted period is 18 months ahead from June 1999. This study s basic ndings are that the series does not reveal any drastic change for the forecasted period. It continues to follow the same trend along with the seasonal variation. I. INTROD UCTIO N Economic growth in a nation is closely related to the availability of energy. Electricity is the most exible form of energy that constitutes one of the vital infrastructural inputs in socio-economic development. Due to increased industrialization and commercialization; the demand for electricity has been growing continuously. Since electricity cannot be stored and there is substantial variation of demand for electricity within a day, between the days and between the months so precise forecasting of demand for electricity is of great importance. This enables the policy maker to plan for cost-e ective investment and operation of the existing and new power plants so that the supply of electricity can be adequate enough to meet the future demand and its variation. Time series forecasting is a sophisticated and widely used technique to forecast the future demand. A time series usually contains secular trends, seasonal variations, cyclical movements and irregular components. Cyclical component, which is basically related to the business cycle movement, causes change considerably over a period of 10 to 15 years. Hence for a short span of time it becomes really di cult to distinguish between the trend and cyclical components in a series. 1 Time series forecasting is a technique that helps to predict what will occur in future if the trends do not change. Univariate time-series analysis incorporates making use of historical data of the concerned variable to construct a model that describes the behaviour of this variable (timeseries) and allows making satisfactory forecast for the future. This paper has tried to forecast the short-run (monthly) maximum electricity demand in Maharashtra, an important state located at the western part of India, by using univariate Box±Jenkins Autoregressive Integrated Moving Average (ARIMA) Technique. ARIMA model has long been used by researchers and modellers in order to forecast the short-run electricity demand (Nelson et al., 1989; Tserkezos, 1992; Kokkelenberg and Mount, 1993; Chavez et al., 1999). The paper is organized in the following manner: Section II contains the theories of ARIMA models. Section III gives description of the data and statistical analysis of the series. Finally, Section IV wraps up the work into conclusion. II. ARIM A MODELS A linear non-stationary stochastic process is said to be homogeneous of degree d when upon di erentiating the original process by d times, the resulting transformed pro- * Corresponding author: Energy Division, CII, Gate No. 31, North Block, J. N. Stadium, New Delhi 110 003, India. E-mail: sajal.ghosh@ ciionline.org 1 In this case it is assumed that the trend includes the cyclical component. So, trend and seasonal components are the permanent components whereas random component captures all idiosyncratic nature of the series. Applied Economics ISSN 0003±6846 print/issn 1466±4283 online # 2002 Taylor & Francis Ltd http://www.tandf.co.uk/journals DOI: 10.1080/00036840110064656 1055

1056 S. Ghosh and A. Das cess has become covariance-stationary. If the original series X t is homogeneous of degree d, then d X t ˆ 1 L d X t ˆ Z t ; t ˆ 1; 2; 3;... ; T 1 is covariance-stationary. Here, L is the backward shift operator. An integrated process X t is designed as an ARIMA (p; d; q), if taking di erences of order d, a stationary process Z t of the type ARMA (p; q) is obtained. The ARIMA (p, d, q) model is expressed by the function Z t ˆ 1 Z t 1 2 Z t 2...... p Z t p u t 1 u t 1 2 u t 2...... q u t q Or L 1 L d X t ˆ L u t 2 Non-stationary homogeneous models with seasonal variations, ARIMA (P,D,Q) s : In most of the monthly electricity time series data, seasonal variation is one of the main sources of non-stationarity. To remove seasonal non-stationarity of such series where seasonality is yearly, one can proceed with seasonal di erencing by s ˆ 12 times. The seasonal models ARIMA (P; D; Q), which are not stationary but homogeneous of degree D can be expressed as Z t ˆ 1 Z t s 2 Z t 2s...... p Z t ps d u t 1 u t s 2 u t 2s... Or p L s 1 L s D X t ˆ d Q L s u t 3 where and are xed seasonal autoregressive (AR) and moving average (MA) parameters. General multiplicative seasonal models, ARIMA (p, d, q) (P, D, Q) 2 s : These models take into account the e ect of trend and seasonal uctuations of a time series and are expressed as: p L s p L 1 L s D 1 L d X t ˆ Q L s q L u t 4 Root mean square error (RMSE) criterion: To evaluate the performance of the model one can consider RMSE criterion, which is de ned as: h RMSE ˆ 1=T X i 1=2 ^X t X t 2 5 where ^X t is the one step ahead forecast or tted value of X t based on an estimated model, and T is the number of observations used in the computation. According to the above de nition the RMSE is an estimate of the standard deviation of random errors (s), if the model is appropriate and the parameter estimates of the model are unbiased. The post-sample RMSE is a measure of model performance of forecast accuracy using the estimated model. Assuming the estimated model is representative during the forecast period, the post-sample RMSE is a guide to assess which model better explains the forecasted time series. ARIMA model building For a given time series, it is important to know which ARIMA model is capable of generating the underlying series. In other words, which model adequately represents the behaviour of the concerned Time Series so that the forecasts of the series under study can be done precisely. Box±Jenkins consider model building as an iterative process which can be divided into four stages: identi cation, estimation, diagnostic checking and forecasting. Identi cation: This stage basically tries to identify an appropriate ARIMA model for the underlying stationary time series on the basis of Sample Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF). If the series is nonstationary it is rst transformed to covariance-stationary and then one can easily identify the possible values of the regular part of the model i.e., autoregressive order p and moving average order q in a univariate ARMA model along with the seasonal part. Estimation: In the estimation stage, point estimates of the coe cients can be obtained by the method of maximum likelihood. Associated standard errors are also provided, suggesting which coe cients could be dropped. Diagnostic checking: In this stage, additional autoregressive and moving average variables can be added and their statistical signi cance can be examined. One should also examine whether the residuals of the model appear to be white noise process. After the model has been respeci ed, it will be reestimated and diagnostic checks will be applied again until the coe cients are reasonably statistically signi cant and the residuals are random. Forecasting: After the diagnostic checking comes the fundamental aim of the methodology, i.e., the forecasts of the future values of the time series. III. DATA D ES CRIPTIO N AND STATISTICAL AN ALYSIS In this article, the variable under study is `maximum monthly electricity demand of Maharashtra from April 2 For a time series having both seasonal and nonseasonal components multiplicative ARIMA type of models are preferred to additive ARIMA.

Short-run electricity demand forecasts in Maharashtra 1057 12000 10000 Mw 8000 6000 4000 2000 0 1 14 27 40 53 66 79 1980 to June 1999. The data have been collected from Maharashtra State Electricity Board. This paper made an attempt to forecast the short-run maximum electricity demand of Maharashtra. The forecast periods are 18 months ahead from June 1999. This study has used simple Box±Jenkins methodology for modelling this variable. The statistical package used for this purpose is `SAS version 6.12. From the raw plot of the time series data, as shown in Fig. 1, it is clear that the series poses nonstationary behaviour along with increasing trend and seasonal variation. In order to make a robust conclusion on the seasonal pattern of the series the level variable is regressed on 12 seasonal dummies. It has been observed that each of the dummy coe cients is signi cantly di erent from zero. 3 So, seasonal component is a systematic cause of variation of the concerned series. But in order to know if seasonal component is the only systematic part, which is causing nonstationarity or whether there is any other systematic component present in the series the classical Box± Jenkins Identi cation procedure is proceeded with. From correlogram (not reported here) it is observed that ACF tails o very slowly at higher lags indicating the presence of nonstationarity in the series. Table 1. Unit root tests of the maximum monthly electricity demand Critical value Origin ADf lag at 10% level signi cance length Adf statistic of signi cance Level 11 0.81117 3.13 First di erence* 15 4.2006 2.57 Notes: * Rejection of null hypothesis of a unit root. 92 105 118 131 144 Months (4/80 to 6/99) Fig. 1. Monthly maximum electricity demand in Maharashtra 157 170 183 196 209 222 Also, inverse autocorrelation function as well as PACF plot show that the autocorrelations are not only signi cant at lag 12, lags 1, 11 and 13 are also signi cant. This gives a clear indication that there must be nonseasonal systematic component, (trend here) making the series nonstationary. Besides, Augmented Dickey±Fuller (ADF) test also assures that the series has nonstationarity. ADF test is conducted with the following model: X t ˆ a 0 bt a 1 X t 1 j X t j " t ; j : 1; 2;... ; p where X t is the underlying variable at time t, " t is the error term and 0 ; ; 1 and j are the parameters to be estimated. The lag terms are introduced in order to justify that errors are uncorrelated with lag terms. For the abovespeci ed model the hypothesis, which would be of interest, is: H 0 : a 0 ˆ 0 and 1 ˆ 0 The results of the unit root tests are reported in Table 1. It has been found that the null hypothesis of unit root is not rejected at the 10% level of signi cance implying that the series is nonstationary. Hence, this study takes the rst di erence of the series and carried out similar analysis (stated above) on the rst di erenced series where the null hypothesis of a unit root is rejected at 10% level of signi cance. Contrary to the unit root tests, which indicate stationarity after taking rst di erence, it has been found that the correlogram associated with the rst di erence series appear to show that the series is still nonstationary. The ACF and PACF still show signi cant spikes 4 at lag 1, 12, 11 and 13 and the rate of decaying in ACF is linear indicating the presence of seasonality as well as nonstationarity. As a result, this study takes rst and span-12 di erence of the series. Identi cation stage con rms stationarity of the series. In the next stage, this study has estimated about 21 models taking di erent values of p and q ranging from 0 to 3 and for seasonal AR and/or MA component P ˆ 0 or Q ˆ 3 respectively. It has been found that ARIMA (0, 1, 3) (0, 12, 1) is the best tted model in terms of smallest Akike Information Criterion (AIC) and Schwarz Bayesiam Criterion (SBC) to explain the maximum monthly electricity demand in Maharashtra. This model has also ful lled RMSE criterion. Hence the estimated model (with absolute t-ratios in parentheses) is: 6 3 Values will be provided on request. 4 A large statistically signi cant autocorrelation is termed as Spike.

1058 S. Ghosh and A. Das Table 2. Diagnostic checking of the estimated model Probability [Table value> Lag Chi-sq(À 2 ) dof Observed (À 2 )] 6 3.60 12 0.16 12 6.18 8 0.62 18 9.12 14 0.82 24 10.51 20 0.95 30 15.33 26 0.95 36 21.37 32 0.92 42 27.88 38 0.88 1 L 1 L 12 X t 1:86 4:94 ˆ 1 0:64L 0:01L 2 0:28L 3 1 0:88L 12 u t 10:21 0:12 4:26 15:98 AIC ˆ 3139:13 SBC ˆ 3156:12 Diagnostic checking of this model shows that the estimated residuals are random as shown in Table 2. Again, the correlogram of the estimated residuals (not reported here) shows that the ACFs are within 95% con dence interval limits. The estimated model is used to forecast monthly maximum electricity demand in Maharhastra for 18 months from June 1999. The forecast series and plot of the same are shown in Table 3 and Fig. 2 respectively. IV. CONCLUS ION Maharashtra has a total geographical area of 308 000 square kilometres. The State has a total population and Mw 12000 10000 8000 6000 4000 2000 0 Jan-98 Jul-98 Feb-99 Aug-99 Mar-00 Oct-00 Apr-01 Months (6/98 to 12/2000) Fig. 2. Electricity demand forecasts in Maharashtra Original Forecast peak electricity demand of 89 million and 9719 Mega- Watt (MW) respectively where as Maharashtra State Electricity Board (MSEB) has a total installed capacity of about 11544 MW in 1998±1999. Agricultural and industrial sector consume about 32 and 34% of the electricity sold respectively. Per capita Gross Domestic Product and per capita electricity consumption are Rupees 20343 and 558 kilo-watt-hour respectively in 1998±1999, which are well above the national level (Economic Survey of Maharashtra 1998±1999). This paper has predicted maximum monthly electricity demand in Maharashtra for 18 months ahead from June 1999. Forecast series have not revealed any drastic change in maximum demand for electricity in the near future. The series appears to follow the same trend along with seasonal variation. The prediction will have minimum forecast error if there is no structural break within the forecast period. Table 3. Electricity demand forecasts in Maharashtra Observation Forecast (Mw) Lower 5% (Mw) Upper 5% (Mw) Jul-1999 10 443.5465 9900.3144 10 986.7785 Aug-1999 10 595.6632 10 019.9272 11 171.3993 Sep-1999 10 356.1805 9748.0314 10 964.3295 Oct-1999 10 512.1545 9902.466 11 121.8431 Nov-1999 10 660.9563 10 049.7322 11 272.1805 Dec-1999 10 773.0345 10 160.2786 11 385.7905 Jan-2000 10 832.1726 10 217.8887 11 446.4565 Feb-2000 10 774.7109 10 158.9029 11 390.519 Mar-2000 10 532.3192 9914.9908 11 149.6477 Apr-2000 10 338.4057 9719.5606 10 957.2508 May-2000 10 346.6709 9726.3129 10 967.029 Jun-2000 10 650.6672 10 028.7999 11 272.5345 Jul-2000 10 752.7069 10 121.6361 11 383.7777 Aug-2000 11 112.0071 10 477.5154 11 746.4988 Sep-2000 10 978.5122 10 340.5547 11 616.4697 Oct-2000 11 136.3473 10 496.5559 11 776.1388 Nov-2000 11 287.0102 10 645.3901 11 928.6303 Dec-2000 11 400.9495 10 757.5058 12 044.3931

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