Time Series Forecasting of Active Power Using ARIMA,SARIMA
and Hybrid Models
Khairul Eahsun Fahim1* , Liyanage C De Silva2 and Hayati Yassin3
1,3 Faculty of Integrated Technologies, Universiti Brunei Darussalam
2 School of Digital Sciences, Universiti Brunei Darussalam
*[email protected] & *[email protected]
Keywords: ARIMA,SARIMA, SARIMAX.
1 Introduction
Because of the increasing availability of time-series data from smart meters and Internet of Things devices, data-driven forecasting techniques are becoming essential. Tradi- tional time-series forecasting models, such as the Autoregressive Integrated Moving Average (ARIMA) and Seasonal ARIMA (SARIMA), have been used in energy and demand forecasting because of their ability to accurately capture temporal correlations in data [1]. Modern power management systems must be able to forecast energy de- mand, especially as the world's energy consumption keeps growing [2]. By forecasting Active Power, utility companies can optimize resource allocation, increase operational efficiency, and ensure reliable service delivery [3].
© The Author(s) 2025
Abstract. This research compares the ARIMA, SARIMAX, and hybrid Holt- Winters with SARIMAX models for projecting Active Power consumption using hourly observational data from January 1, 2023, to December 31, 2023. For ef- fective energy management and resource allocation in situations with fluctuating demand, an accurate Active Power forecast is essential. By evaluating each mod- el's performance using RMSE, MAE, and MAPE measures, distinct benefits and drawbacks are shown. In short-term projections, the ARIMA model's low RMSE and MAE demonstrated accuracy, despite its MAPE indicating variability con- cerns. However, SARIMA's performance was balanced across all parameters, in- dicating that it is appropriate for data that exhibits seasonal tendencies. The en- semble stacking model enhanced RMSE, which suggests that increased forecast- ing capabilities come at the expense of additional processing power.
S. Singh et al. (eds.), Proceedings of the Smart Sustainable Development Conference 2025 (SSD2025), Atlantis Highlights in Sustainable Development 2,
https://doi.org/10.2991/978-94-6463-720-5_18
However, these models could struggle to handle complex seasonal patterns and data fluctuations, especially in dynamic environments where environmental and operational factors influence power consumption [4]. Extensions of these models, such as SARIMAX [5] (Seasonal ARIMA with Exogenous Variables), improve predictive power by including additional variables in scenarios where exogenous influences are present. Furthermore, hybrid models that combine methods like Ensemble Stacking with XGBoost have the potential to more accurately capture both seasonal and trend components [6], particularly in datasets with considerable seasonality and volatility.
This study compares the hourly Active Power forecasting performance of ARIMA, SARIMAX, SARIMA, and a hybrid Holt-Winters and SARIMAX model using data collected from January 1, 2023, to December 31, 2023. This dataset contains hourly measurements from 7:00 to 18:00 every day in addition to Active Power, which capture significant solar and weather-related features. To find out more about the accuracy and reliability of each model, its performance was evaluated using measures such as Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and Root Mean Square Error (RMSE).
The primary aim and objective of this paper are twofold: first, by comparing the models and assessing their prediction accuracy and suitability for energy forecasting. Accord- ing to our findings, hybrid strategies might be more beneficial for dealing with seasonal.
2 Literature Review
Time-series forecasting has been extensively studied in relation to energy consumption prediction. The ability of models like ARIMA, SARIMA, and hybrid approaches to accurately capture temporal patterns and seasonality in data makes them widely em- ployed. ARIMA models are a standard in time-series analysis because of their ability to explain non-stationary data via differencing, which was initially demonstrated by Box and Jenkins. Numerous studies have employed ARIMA for energy forecasting, demonstrating its interpretability and ability to control short-term reliance. However, in order to effectively capture such periodicities, ARIMA models may need to be changed because they do not naturally integrate seasonal components.
Using seasonal autoregressive and moving average terms to account for seasonality allows SARIMA models to capture periodic swings in data. SARIMA has been widely used to forecast energy demand in situations with significant seasonal cycles, such as daily and weekly consumption patterns in power networks. Studies on renewable en- ergy systems, such as solar and wind power, have successfully used SARIMA to fore- cast output because of its ability to account for the inherent seasonality of these sources.
However, SARIMA may struggle with volatile data or datasets affected by external factors, like weather, which are often present in power consumption statistics.
The SARIMAX model builds on SARIMA by including exogenous variables, which is particularly useful when the target variable is significantly influenced by external fac- tors. For instance, energy consumption studies often include variables like temperature, humidity, and sun radiation to improve prediction accuracy. Beyond seasonality, exog- enous variables provide additional information that enhances the model's performance
by helping to capture the impact of external events. Even while SARIMAX improves SARIMA by integrating external information, it may still have issues when working with highly volatile datasets since complex, non-linear interactions might cause it to overfit or underfit.
The proposed stacking ensemble strategy uses XGBoost as the meta-learner and outputs from multiple deep learning models (LSTM, Bi-LSTM, GRU, CNN-BiLSTM, CNN-BiGRU, and Bi-GRU) as base learners to increase regression accuracy for time dependent data [7]. By stacking the predictions of each base model, which independently captures temporal dependencies, the meta-learner generates the final predictions.
Metrics including RMSE, MAE, MAPE, and R2 are used to evaluate performance in addition to denormalized measurements for interpretation on the original scale. The stacking ensemble performs better in terms of accuracy than ARIMA, SARIMA, SARIMAX, and hybrid Holt-Winters models by utilizing the range of predictions from base models and minimizing biases and errors. As a result, it excels in time series forecasting tasks involving complex temporal patterns.
The advancement of machine learning techniques in recent years has led to an in- crease in the depth of the literature on energy forecasting. Because of their interpreta- bility, computational efficiency, and ability to handle smaller datasets, classical statis- tical models like ARIMA, SARIMA, and hybrid models are still often utilized. Accord- ing to scopus advanced search not much research has been done in the recent past using ensemble stacking algorithm which combines predictions from multiple base algorithm for finding time Series Forecasting of Active Power. This work adds to the body of literature by comparing the ARIMA, SARIMAX, SARIMA, hybrid Holt-Winters, SARIMAX, and ensemble stacking models in an effort to clarify the benefits and draw- backs of each approach for hourly Active Power consumption prediction.
3 Methodology
Hourly Active Power consumption measurements and other weather-related data for each hour between 7:00 and 18:00 between January 1, 2023, and December 31, 2023 comprise the dataset used in this study. Data was collected from the Universiti Brunei Darussalam- Faculty of Integrated Technologies rooftop solar system. The following steps outline the methodology for data preprocessing, model training, and evaluation.
3.1 Data Processing
Barometric pressure, temperature, humidity, sun radiation, and cooling degree days were among the features in the dataset, which was initially cleaned to remove any miss- ing values or anomalies. Care was taken when imputation of data because continuity is important in time-series forecasting. Scaling procedures such as standardization and min-max scaling were employed to ensure that each feature contributed appropriately to the training of the model. Active Power, the aim variable, was kept as a continuous variable to retain the model's forecast accuracy.
𝜃𝑗 are the moving average parameters 3.2 Model Selection and Parameter Tuning
Model selection and parameter tuning plays an important role in finding the accuracy of the model. Some of the models used in this paper are ARIMA, SARIMA, SARIMAX, Hybrid Holt Winters are explained below
3.2.1 ARIMA Model
A moving average, differencing to address non-stationarity, and historical data are all used in the AutoRegressive Integrated Moving Average (ARIMA) model to forecast a time series variable. (p,d,q) represents the general ARIMA model formula, which is [8]
𝑌𝑡= 𝑐 + ∅1𝑌𝑡−1+ ∅2𝑌𝑡−2+ ∅𝑝𝑌𝑡−𝑝+ 𝜃1∈𝑡−1+ 𝜃2𝜖𝑡−2+ ⋯ + 𝜃𝑞𝜖𝑡−𝑞+ 𝜖𝑡 (1) Where
𝑌𝑡 is the value of time t 𝑐 is a constant
∅𝑖 are the auto regressive parameters ∈𝑡 is white noise
The Bayesian Information Criterion (BIC) and Akaike Information Criterion (AIC) scores were used to optimize the ARIMA model's parameters [9]. The ARIMA model's predicted and real Active Power values are shown in Figure 1.
3.2.2 SARIMA Model
The ARIMA model is expanded to include seasonal components in the SARIMA model. The letters p, d, and q stand for the SARIMA model. where s is the seasonal period and P, D, and Q stand for the seasonal autoregressive, differencing, and moving average terms [10].
SARIMA model equation is denoted with
(1 − ∅𝐵)(1 − Φ𝐵𝑠)𝑌𝑡= (1 − 𝜃𝐵)(1 − Θ𝐵𝑠) ∈𝑡 (2) Where
B is the backshift operator
Φ and Φ are the autoregressive terms 𝜃 and Θ are the moving average terms 3.2.3 SARIMAX Model
In order to capture the impact of outside factors (such as temperature and solar radia- tion) on the target variable, SARIMAX integrates exogenous variables into SARIMA[11]. By adding an exogenous variable factor, the SARIMAX model equation extends SARIMA.
𝑌𝑡= 𝛼 + 𝛽𝑋𝑡+∈𝑡 (3) Where 𝑋𝑡 represents the exogenous The exogenous variables at time 𝑡 are represented with a coefficient β, contributing external explanatory power to the model. Figure 3
depicts the SARIMAX model's performance, specifically how it alters predictions based on exogenous inputs
3.2.4 Hybrid Holt Winters and SARIMAX model
Holt-Winters seasonal smoothing and SARIMAX are combined in the hybrid model to capture seasonal patterns and trends through decomposition [12]. The following is how Holt-Winters exponential smoothing calculates the level, trend, and seasonal compo- nents:
𝐿𝑡= 𝛼(𝑌𝑡− 𝑆𝑡−𝑠) + (1 − 𝛼)(𝐿𝑡−1+ 𝑇𝑡−1) (4) 𝑇𝑡= γ(𝐿𝑡− 𝐿𝑡−1) + (1 − γ)𝑇𝑡−1 (5)
𝑆
𝑡=
δ(
𝑌𝑡− 𝐿𝑡)
+ (1 − δ)𝑆𝑡−𝑠 (6) Where𝐿𝑡 is the level component 𝑇𝑡 is the trend component 𝑆𝑡 is the seasonal component 𝛼, 𝛾 𝑎𝑛𝑑 𝛿 are smoothing parameters
The smoothed series is then sent into SARIMAX, which generates predictions that take into account complicated seasonality. Figure 4 shows the hybrid model's forecast vs actual Active Power values.
3.2.4 VARIMA Model
A potent statistical framework for modeling and predicting multivariate time series, Vector AutoRegression (VAR) captures the dynamic interdependence of variables [13].
A system of equations where each variable is a linear function of its own lagged values and the lagged values of all other variables is produced by VAR, which treats all vari- ables as endogenous in contrast to univariate autoregressive models. The following is a mathematical version of the VAR (p) model for k-dimensional time series.
𝑦𝑡= 𝑐 + ∑𝑝𝑖=1𝐴𝑖𝑦𝑡−𝑖+ 𝑢𝑡 (7) Where
𝑐 is a vector of intercepts
𝐴𝑖 are coefficient matrices for observing the lagged variables 𝑢𝑡 is a white noise error vector with covariance matrix ∑ 𝑢
Ordinary Least Squares (OLS) is commonly used to estimate the model's parameters, and the Bayesian Information Criterion (BIC) or Akaike Information Criterion (AIC) are used to find the appropriate lag order (p). Short-term forecasting, in which predic- tions are produced iteratively using lagged values, benefits greatly from VAR's ability to capture linear interdependencies.
Nevertheless, its use is predicated on the time series' stationarity, and the more dimen- sional the data, the higher the processing requirements. Notwithstanding these draw- backs, VAR is still a frequently utilized tool in finance and economics, fields where it is essential to comprehend and forecast how many variables will interact.
Using known values for 𝑦𝑡, 𝑦𝑡−1, … . , 𝑦𝑡−𝑝+1 to predict the value of 𝑦𝑡+1 Use predicted 𝑦𝑡+1 for computing the 𝑦𝑡+2
3.2.5 VAR model
Iteratively, the VAR(𝑝) model is used to make forecasts for subsequent time steps (𝑡+ℎ). The following steps are used to forecast using a VAR model [14]
a.
b.
The j-step ahead forecast is given by
𝑦
𝑡+ℎ= 𝑐 + 𝐴
1𝑦
𝑡+ℎ−1+ 𝐴 ̂
2𝑦
𝑡+ℎ−2̂ + ⋯ + 𝐴 ̂
𝑝𝑦
𝑡+ℎ−𝑝̂
(7)
The capacity to capture dynamic interdependencies among numerous variables and the success of Vector AutoRegression (VAR) in short-term forecasting for multivariate time series are just two of its many benefits. The assumption of linear correlations be- tween variables, the need for data stationarity, and the possibility of computational complexity in high-dimensional datasets are some of its drawbacks. In disciplines like economics and finance, where comprehending and predicting multivariate time series is crucial, VAR is still a commonly used tool in spite of these difficulties.
3.2.6 Stacking Ensemble Algorithm
The proposed method employs a stacking ensemble framework to improve predictive accuracy in regression tasks. It combines the outputs of multiple deep learning models with various architectures, including LSTM, Bi-LSTM [15], CNN-BiLSTM [16], GRU, CNN-BiGRU[17], and Bi-GRU [18], with XGBoost serving as the meta-learner.
Each of the base models 𝑀𝑖 (where the values of 𝑖 ranges from 1 𝑡𝑜 𝑛) is independently trained on the training dataset 𝑗𝑡𝑟𝑎𝑖𝑛 = {(𝑋𝑡, 𝑦𝑡)}𝑡=1𝑇 where input feature is denoted with 𝑋𝑡 and the target variables are denoted with 𝑦𝑡 . 𝑀𝑖 responsible for capturing the tem- poral dependencies. 𝑦⏞𝑖𝑡𝑒𝑠𝑡 = 𝑀𝑖(𝑋𝑡𝑒𝑠𝑡) for the test dataset which is denoted with 𝑋𝑡𝑒𝑠𝑡.
𝑦⏞𝑓𝑖𝑛𝑎𝑙= 𝑀𝑚𝑒𝑡𝑎(𝐽𝑠𝑡𝑎𝑐𝑘) (8)
R
2=1-
∑Nt=1(y
t- y
⏞t)2∑Ni=1(
y
t-y
̅)2 (9) MSE=1N ∑Nt=1(yt- y⏞ )t 2 (10) RMSE=√MSE (11) 𝑀𝐴𝐸 =1
𝑁 ∑𝑁𝑡=1|𝑦𝑡− 𝑦⏞ |𝑡 (12) To create a new dataset all the predictions 𝑦̂𝑖𝑡𝑒𝑠𝑡 coming from the base models are combined column wise. 𝐽𝑠𝑡𝑎𝑐𝑘 = 𝑦⏞1𝑡𝑒𝑠𝑡, 𝑦⏞2𝑡𝑒𝑠𝑡, … . , 𝑦⏞𝑛𝑡𝑒𝑠𝑡 . Output of the specific base models are denoted with the each corresponding columns. The meta learner 𝑀𝑚𝑒𝑡𝑎 takes the stacked dataset as input. 𝑀𝑚𝑒𝑡𝑎 is an XGboost regressor which is trained on 𝐽𝑠𝑡𝑎𝑐𝑘 and the actual target values are denoted with 𝑦𝑡𝑒𝑠𝑡. The mapping of the meta learner is denoted with 𝑀𝑚𝑒𝑡𝑎: 𝐽𝑠𝑡𝑎𝑐𝑘→ 𝑦𝑡𝑒𝑠𝑡 which produces the final predictions
𝑀𝐴𝑃𝐸 =100
𝑁 ∑ |𝑦𝑡− 𝑦⏞𝑡
𝑦𝑡 | (13)
𝑁
𝑡=1
N stands for the number of test samples. The symbols 𝑦𝑡, 𝑦̅𝑡 and 𝑦 stand for goal values, predicted values, and the mean of the true target values, respectively. Furthermore, in order to interpret flaws in the original scale 𝑦𝑚𝑎𝑥− 𝑦𝑚𝑖𝑛,denormalized metrics are computed using the range of the target variable. The stacking ensemble beat the indi- vidual base models by effectively utilizing 𝑀𝑚𝑒𝑡𝑎 to leverage the diversity of model predictions, proving its ability to reduce biases and errors. This illustrates the efficacy of stacking ensembles in solving regression issues, especially when working with data that is dependent on time.
4 Results
The forecasting of "Active Power" using the ARIMA model had mixed results, alt- hough it did well in terms of RMSE (0.048) and MAE (0.039), demonstrating that it could predict both absolute and squared deviations with accuracy. Although the da- taset's near-zero or zero values can disproportionately inflate MAPE, the abnormally high MAPE score suggested issues with the % error calculations. Plotted comparisons demonstrated that the forecasts and actual values visually aligned, and the ARIMA (1, 1, 1) model was selected because it was able to represent the underlying trend and dif- ferencing needs of the time series. Especially for short-term forecasting, these results show how effective ARIMA is at modeling univariate time series data
Fig 1 Results obtained from the ARIMA model
Figure 2 illustrates how the SARIMA model's reasonable forecasting performance for "Active Power," with an RMSE of 0.7366 and an MAE of 0.6201, demonstrated its ability to closely match forecasts with actual values and successfully capture underlying trends and seasonality. However, the extremely high MAPE, which is likely caused by near-zero or zero values in the dataset that disproportionately inflate MAPE estimates, highlights a severe issue with percentage error estimation. This highlights how im- portant it is to have distinct evaluation criteria when working with datasets of this type.
However, abrupt peaks and troughs are accompanied by minor variations, as is com-
things change quickly.
With the model's predicted values (yellow) almost exactly matching the actual values (blue), the accompanying graph demonstrates how well the SARIMA model captures temporal patterns
Fig 2 Actual versus SARIMA model-predicted values
The Hybrid Holt-Winters + SARIMAX model's forecasting skill for "Active Power,"
as measured by its RMSE of 1.15, is low, implying that it can fairly match forecasts with observed values. Figure 3 makes clear that by combining the benefits of Holt- Winters' seasonal decomposition with SARIMAX's ability to depict temporal correla- tions, the hybrid technique effectively captures the trend and seasonality of the data.
The graph shows a high degree of agreement between the expected values (orange) and the actual values (blue), especially for broad trends and seasonal changes.
Fig 3 Actual Vs Predicted values obtained from Hybrid Holt-Winters + SARIMAX The SARIMAX model's RMSE of about 1.20 indicates that it can predict "Active Power" over the given time frame. Figure 4's graph comparing the actual and expected mon in time series models dealing with high variability or extreme values. With Holt- Winters conquering seasonality and SARIMAX boosting long-term dependencies, this hybrid model leverages the complementary strengths of its component elements, mak- ing it suitable for scenarios with complex temporal patterns. Even while the perfor- mance is good, it may be even more accurate in terms of prediction with a few little tweaks or the addition of other ensemble techniques, particularly in situations where
Fig 4 Actual versus SARIMAX model-predicted values
values shows how closely the SARIMAX predictions match the observed values, par- ticularly when it comes to spotting broad trends and seasonal patterns. The inherent limitations of the model in handling large variations, however, are to be expected be- cause certain discrepancies are noticeable, especially during peaks and rapid fluctua- tions. SARIMAX is an excellent choice for prediction tasks because it successfully captures the underlying temporal dynamics of the time series, as evidenced by the con- sistent match between the forecasts and actual data for much of the range. Despite its ability to accurately detect patterns and seasonality.
The use of VARIMA to forecast "Active Power" from the given dataset demon- strated its ability to capture temporal relationships among a large number of associated characteristics. After a thorough grid search across a number of parameters, the optimal VARIMA order was found to be (0,1,0), which produced the lowest RMSE of 1.564.
The dataset was normalized for improved numerical stability and preprocessed with forward filling for missing values. Included were significant characteristics like tem- perature, sun radiation, and barometric pressure. Despite convergence warnings and problems with its robustness, the VARIMA model's efficacy was demonstrated by the forecasts' near-match with the test set's actual values. Forecasting for January 1, 2024, based on historical trends, produced accurate estimates, and the shift from December 31, 2023
The ability of many deep learning models and their stacking ensemble equivalent (XGBoost) to predict the target variable is illustrated by the findings in Figure 5. With R squared scores ranging from 0.67 to 0.70, each deep learning model—including LSTM, Bi-LSTM, CNN-BiLSTM, GRU, CNN-BiGRU, and Bi-GRU—exhibited re- spectable prediction abilities on its own. In terms of normalized RMSE (∼0.166) and MAE (∼0.128), the LSTM and CNN-BiLSTM architectures scored better than the oth- ers, suggesting somewhat better performance. However, MAPE (Mean Absolute Per- centage Error) was a major problem for all of these models, leading to infinite because of division by zero or very small values in the dataset. This illustrates how using MAPE on datasets with near-zero or zero goal values is restricted
model may identify patterns and trends.
Fig 5 Decomposition of Hourly Demand over a Year
None of the individual models could match the performance of the XGBoost stack- ing ensemble model. As evidenced by its nearly perfect R^2 score of 0.99996, it ex- plained virtually all of the variance in the target variable. The ensemble model's nor- malized RMSE and MAE values were significantly lower, at 0.0018 and 0.0012, re- spectively. With an RMSE of 0.0099 and an MAE of 0.0068, the denormalized RMSE and MAE values provide more evidence of the ensemble model's correctness. Because the stacking ensemble effectively used the benefits of each individual model to achieve impressively precise results, these results demonstrate the stacking ensemble's superior prediction capabilities.
Fig 6 From October 16 to October 19, 2023, Active Vs. forecasted electricity generation utilizing ensemble stacking
The actual hourly readings from December 25, 2023, to December 31, 2023, are shown in blue in Figure 7. The superiority of this hybrid method is demonstrated by the The information in Figure 6 compares the actual and anticipated power generation for the dates of October 16–19, 2023. The graph clearly shows that, on the dates of October 16–17, the expected value and the actual value are nearly equal. On October 17, there were a few minor undershots. Although the anticipated data for October 18th can follow trends and capture them, it does not overlap as closely as the data from the prior two days. Predicted values for nearly every timestamp on October 19th overlap with the actual data. The comparative graph makes it clear that the ensemble stacking
graph, which shows that the hourly projected values, indicated in red, are nearly exactly in line with the actual data from the previous week
Figure 7 shows the hourly solar power generation on January 1, 2024, as well as the previous seven days.
Figure 8 displays a time series breakdown of the data used in the stacking ensemble approach, identifying four components: trend, seasonal, residual, and observed. The trend component, represented by the blue line, illustrates the long-term upward and downward movements of the data as well as gradual alterations over time that were most likely influenced by external factors. The seasonal component, represented by the green line, exhibits regular and periodic oscillations, indicating repeating patterns within predefined intervals. The residual component, shown by the red line, reveals erratic fluctuations or random noise that cannot be accounted for by trend or seasonal- ity, leading to unexpected spikes. The observed component, which combines all of these elements to display the overall behavior of the raw data, is finally represented by the black line.
Fig 8 Seasonal Decomposition obtained from Ensemble Stacking model The notable improvement in performance with the stacking ensemble suggests that combining many model designs can improve overall predictions and mitigate the draw- backs of individual models. However, MAPE performs badly across all models due to
the dataset's features, highlighting the need for careful selection of evaluation measures that are robust to zero or almost zero goal values. Future efforts to enhance model as- sessment and metric selection may be guided by this conclusion.
ARIMA and VARIMA are significantly outperformed by the stacking ensemble model (XGBoost). With low normalized RMSE (0.048) and MAE (0.039), ARIMA offers a respectable predictive capacity for short-term univariate forecasting. However, because of the dataset's near-zero values, which emphasize its sensitivity to extreme values, it suffers from high MAPE. Similar to ARIMA and the stacking ensemble, VARIMA, which was developed for multivariate forecasting, effectively captures tem- poral correlations and accounts for pertinent variables like temperature and sun radia- tion; nevertheless, its normalized RMSE (1.564) indicates lower accuracy. Moreover, it encountered issues like convergence warnings. With a low normalized RMSE (0.0018), MAE (0.0012), and a nearly perfect R squared score of 0.99996, the stacking ensemble model performs better.
The effectiveness of a number of forecasting models, including the deep learning- based stacking ensemble, ARIMA, SARIMA, SARIMAX, and VARIMA, in predicting hourly Active Power usage using a rich time-series dataset was examined in this sec- tion. Based on how well-suited each model was for specific scenarios and data kinds, each model displayed unique benefits and drawbacks. Traditional models like SARIMA and ARIMA consistently performed well in capturing seasonality and trends.
They struggled, nevertheless, with datasets with high variability or values that were close to zero. Advanced models like VARIMA showed limitations in accuracy and re- silience due to computational challenges, even if they used multivariate dependencies.
The stacking ensemble model, which included the benefits of multiple deep learning architectures, was the most dependable and accurate forecasting method. Its almost per- fect R2 score, together with its exceptionally low RMSE and MAE, shows that it can minimize prediction errors while including a range of temporal patterns, trends, and seasonality. This improved performance demonstrates how ensemble approaches can overcome the limitations of individual models, making them a desirable choice for dif- ficult time-series forecasting issues.
Future studies could look into further ensemble model optimization, combining more complex topologies and hyperparameter tuning, to increase predicted accuracy. Addi- tionally, developing alternative evaluation metrics that can handle datasets with nearly zero values might improve the assessment of model performance under challenging circumstances. All things considered, the study's conclusions demonstrate how im- portant advanced forecasting techniques are to modern energy management, paving the way for more efficient resource utilization and complicated and dynamic decision-mak- ing
Table 1 Comparative analysis between ARIMA, VARIMA and Stacking Ensem- ble
Discussion
Different forecasting models have unique advantages and disadvantages, which makes them appropriate for particular uses. With a low Normalized RMSE (0.048) and MAE (0.039), ARIMA (1,1,1) is good at capturing trends and short-term forecasting.
However, it has trouble with extreme values and datasets that are close to zero, which results in incorrect MAPE. With a Normalized RMSE of 0.7366 and MAE of 0.6201, SARIMA accounts for seasonality; nonetheless, it has issues with high variability and significant percentage mistakes. With a Normalized RMSE of 1.15, the Hybrid Holt- Winters + SARIMAX model combines Holt-Winters for seasonality and SARIMAX for trends, however it has slight problems with extreme peaks and troughs. Despite its ability to capture seasonality and patterns, SARIMAX struggles with quick changes and has a comparatively high Normalized RMSE (~1.20). VARIMA (0,1,0) is less re- silient because to its high Normalized RMSE (1.564) and convergence warnings, but it does provide multivariate forecasting. With a Normalized RMSE of ~0.166 and MAE of ~0.128, deep learning models like LSTM show greater adaptability and successfully capture complicated patterns. However, they are vulnerable to MAPE because of their near-zero values and need a large amount of processing power. With a remarkably low Normalized RMSE (0.0018), MAE (0.0012), and R2 score of 0.99996, the Stacking Ensemble method with XGBoost performs better than any other model. It provides in- credibly accurate predictions, but it requires significant processing expenses and careful tuning to prevent overfitting. The forecasting needs, available computing power, and the trade-offs between accuracy and interpretability ultimately determine which model is ideal.
Conclusion
Several time-series models for forecasting hourly Active Power use were assessed in this study. Though they had trouble with volatility and near-zero values, traditional models like ARIMA and SARIMA were good at capturing trends and seasonality. The hybrid Holt-Winters and SARIMAX model balanced seasonal trends but was less ac- curate at managing abrupt swings, whereas SARIMAX increased accuracy with exog- enous variables.
VARIMA used multivariate dependencies, however it was less accurate and had computing issues. With an RMSE of 0.0018 and an R-squared score of 0.99996, the stacking ensemble model—which incorporates deep learning architectures with XGBoost—performed better than all other models, exhibiting improved prediction ac- curacy and generalization.
The results demonstrate how ensemble learning is superior to standard models, es- pecially when dealing with complicated datasets. Ensemble approaches offer a more reliable answer, even though ARIMA and SARIMA are still helpful for interpretable short-term forecasting. To increase forecasting accuracy for dynamic energy systems, future studies should improve assessment criteria and ensemble models.
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