Simple exponential smoothing is the most widely used model in forecasting if there are no cyclic variation patterns or consistent growing patterns involved. ¹⁴ The formula for this method is as follows ¹⁸ : F t + m = α y t + 1 − α F t (1)

where:

F t + m : simple exponentially forecast value in period m, for m = 1 , 2 , 3 , … t ; y t : actual value in time t;

α : unknown smoothing constant to be determined for value between 0 and 1;

F t : forecast value at period t.

Holt’s exponential smoothing can be used in forecasting when there is a linear trend in the historical data of the forecast. According to Alias, ¹⁹ this method requires three equations which are exponential smoothed series, trend estimate, and forecast.

Exponential smoothed series: S t = α y t + 1 − α S t − 1 + T t − 1 (2)

Trend estimate: T t = β S t − S t − 1 + 1 − β T t − 1 (3)

Forecast for m period: F t + m = S t + T t × m (4)

where:

S t : exponential smoothed series;

T t : trend estimates;

F t + m : forecast for m-step-ahead period.

This method is also known as the double exponential smoothing and can be used if there is a linear trend in the data. The trend is a smoothed estimate of average growth at the end of each period. ¹⁷ The formula for Brown’s exponential smoothing is as follows: F t + m = α y t + 1 − α F t (5) a t = 2 S t − S t ′ (6) b t = α 1 − α S t − S t ′ (7) S t = α y t + 1 − α S t − 1 (8) S t ′ = α S t + 1 − α S ′ t − 1 (9) where:

S t : exponentially smoothed value of y t at time t;

S t ′ : double exponentially smoothed value of y t at time t;

a t : computes the difference between the exponentially smoothed values;

b t : computes the adjustment factor;

F t + m : forecast for m-step-ahead period.

According to Kalekar, ¹⁷ the forecasting model should be validated. Here, an error measurement such as mean absolute percentage error (MAPE), relative mean square error (RMSE), or mean absolute error (MAE) is needed. The selection of an error measurement has a significant effect in determining the most accurate forecasting method. In this study, MAPE was selected to verify the model because it is the most suitable measurement to compare the accuracy of the forecasting methods, as it measures relative performance. ^{7 , 14 , 20} A low MAPE score indicates that the forecasting model has a good performance. ²¹ The range of the MAPE score is shown in Table 1.

The simple exponential smoothing was analysed using SPSS version 26 (IBM SPSS Statistics, RRID:SCR_019096) starting from the year 2019. Referring to Figure 2, the three lines represent the limit of the forecast values for the forecast year: yellow indicates the upper limit of electricity consumption, purple indicates the best prediction of electricity consumption, and brown indicates the lower limit of electricity consumption at a particular year. This means that the expected electricity consumption could fall between the green and brown dotted lines.

Based on Table 3, the year 2019 recorded the best forecasted electricity consumption, which is 2553 ktoe; the consumption maintains this value until 2032. However, this method also predicted a wide range of possible values until 2032. For example, the electricity consumption in 2032 is predicted to be between 3345 ktoe as the upper limit and 1760 ktoe as the lower limit, but the best value generated is 2553 ktoe.

The accuracy of the forecasting value was measured via model fit statistics. As shown in Table 4, there are three error measurement scores generated by SPSS version 26: relative mean square error (RMSE), mean absolute percentage error (MAPE), and mean absolute error (MAE). For simple exponential MAPE, the score is 5.678.

Figure 3 shows Holt’s exponential smoothing method, which was conducted. It is expected that the electricity consumption value would fall between the pink and brown dotted lines for the forecast year, but the width is narrower compared to the previous method. It can be observed that the forecast has a considerable upward trend from 2019 until 2032.

The value of the best forecasted electricity consumption was 2647 ktoe for 2019 and 3873 ktoe for 2032 as shown in Table 5. In 2032, the predicted electricity consumption value would be between 3360 and 4386 ktoe whereas the best projected value is 3873 ktoe. Table 6 shows the accuracy of the forecasting where the score measured by MAPE is 2.299.

The last forecasting method is Brown’s exponential smoothing ( Figure 4). This method enjoys a very wide range of forecasting values where the upper and lower limit values experienced a steep trend. In 2019, the forecasted electricity consumption value is 2402 ktoe. However, the value gradually decreases year by year until 2032 with a consumption value of 2399 ktoe as presented in Table 7. In 2032, the predicted electricity consumption value would be within 4967 ktoe as the maximum value and 90 ktoe as the minimum value; the best projected value is 2399 ktoe. Table 8 shows the MAPE score for Brown’s exponential smoothing, which is 3.125. The lower the MAPE score, the higher the accuracy of the forecast.