Integrating Pearson Correlation and Hybrid Models for Renewable Energy Demand Prediction in Turkey: 2025–2030 Case Study

1. Introduction

In a globalizing world, increasing population rates, industrialization, technological advancements, and the decline of energy supply resources are pushing energy issues to the forefront of the world's agenda. Numerous studies are being conducted in countries to address this issue. These include energy demand forecasting studies and demand management, energy supply security studies, renewable energy applications, and the analysis and direction of energy policies. Energy demand forecasting is a prominent example of this type of research.

Energy demand forecasting is the estimation of energy demand over specific time frames, taking into account future data and changing parameters. Forecasting studies provide short-term, medium-term, and long-term energy consumption and production plans, providing roadmaps for countries, policymakers, and individual and corporate consumers.

The purpose of energy demand forecasting is to achieve supply-demand balance, implement infrastructure plans, create optimal sizing by considering peak and trough loads, increase energy efficiency, and develop plans for achieving carbon neutrality.

Energy demand forecasting studies are classified according to time scale and forecasting methods. Studies conducted based on time scales are categorized into three categories: short-term, medium-term, and long-term. Short-term studies utilize intraday, day-ahead, and balancing market data to generate hourly and daily forecasts. Medium-term forecasting models utilize monthly and annual forecasts. Long-term models utilize forecasts for periods of 3, 5, 10, or longer.

Energy demand forecasts are categorized into four types based on forecasting methods: statistical methods, machine learning methods, artificial neural network models, and hybrid models.

Numerous studies have been conducted in the literature using forecasting methods. Time series modeling is among the traditional methods in this field. ARIMA, SARIMA, and similar techniques, in particular, have provided effective solutions for identifying historical patterns (Dudek, 2020), (Lee & Cho, 2021),( Sharma & Verma, 2023). However, the fact that these models are based on linear assumptions and cannot adequately reflect the impact of sudden changes and external factors has led to the need for more flexible models. Some studies have shown that statistical methods can provide similar levels of accuracy in certain scenarios compared to artificial neural network models (Zhang & Zhou, 2020),( Yılmaz, 2023).

Machine learning algorithms are frequently applied in energy demand forecasting. Methods such as SVR, Random Forest, and decision trees, in particular, have demonstrated success in learning nonlinear relationships, (Li, Zhang & Chen, 2024),( Al-Qahtani, Elleithy & Alotaibi, 2021),( Sarkar, Roy & Das, 2022).There are examples in the literature where prediction accuracy has been significantly improved by optimizing support vector regression models with genetic algorithms . Furthermore, feature engineering approaches applied to variable selection have also been shown to increase model performance (Al-Qahtani, Elleithy & Alotaibi, 2021), (Kumar, Ranjan & Tiwari, 2023).

Deep learning architectures are one of the areas where the most remarkable advances in energy forecasting have been made. Network structures such as LSTM, GRU, and CNN-LSTM produce effective results on time-dependent data (Roy, Maity & Ghosh, 2021),( Doğan, Kaya & Öztürk, 2024),( Khan, Taj & Smith, 2024). Thanks to the powerful structure of LSTM in sequential data analysis, it has become possible to model the long-term effects of past data . Furthermore, it has been reported that short-term sudden changes in hybrid structures can be successfully learned by integrating LSTM and CNN (Mehmood & Iqbal, 2022).

Hybrid systems that combine different model structures offer the advantages of both statistical components and artificial intelligence models. When seasonal decomposition-based models such as Prophet are combined with deep learning techniques such as LSTM, different dynamics in time series can be analyzed separately (Akçay & Altuğ, 2024). These approaches have enabled higher accuracy rates, especially in regions where seasonal effects are pronounced or sudden demand fluctuations are frequently experienced (Arif & Hussain, 2023),( Akçay & Altuğ, 2024).

Current research trends propose more accurate modeling of energy demand not only with historical consumption data but also with multiple data sources such as climate data, economic indicators, social mobility, and electric vehicle usage statistics . Such multivariate models have made significant contributions to predicting changing consumption habits, especially in the post-pandemic period (Wang, Yu & Zhang, 2023).

Transformer models, one of the new-generation neural network structures, have recently been incorporated into the energy estimation literature. Their success in learning long-term dependencies demonstrates that they have more advanced estimation capabilities compared to classical LSTM or GRU architectures (Kim, Jang & Lee, 2024). Research conducted in the context of Turkey also reflects these global trends. Studies that have presented comparative analyses of methods such as LSTM, Prophet, ARIMA, and Random Forest applied to different regions have demonstrated that hybrid approaches provide superior performance, particularly in short-term forecasting (Demirtaş & Şahin, 2024).It is also emphasized that models adapted to local datasets can produce more effective results than universal models.

A study in (Wang & Li, 2020), analyzed China's electricity demand using the ARIMA model, demonstrating the model's short-term forecasting success. (Alwee, Yusof & Ismail, 2014) compared Exponential Smoothing methods with different parameter sets, achieving high accuracy in industrial consumption forecasts, particularly with the Holt-Winters model. (Mohamed & Kamel, 2015), compared linear regression and an MLP-based artificial neural network, demonstrating that the artificial neural network significantly reduces error rates compared to the linear model. In (Şahin & Karabacak, 2018), Türkiye's annual electricity consumption was modeled using Polynomial Regression, and it was determined that 3rd-degree polynomials gave more appropriate results. In (Zhang, Zhou & Chen, 2020), Lasso and Ridge Regression were tested together, and their performance against overfitting was measured; it was shown that Lasso provided an advantage in terms of variable selection. In (Khosravi, Ghadimi & Dehghanian, 2019), consumption data were modeled using the Random Forest method, and it was shown that the model learned seasonal effects particularly well. In (Ahmad & Chen, 2017), energy demand was estimated using SVR (Support Vector Regression), and better prediction performance was obtained with the RBF kernel compared to other kernel functions. In (Liu, Wang & Zhang, 2019), energy consumption was estimated using the XGBoost algorithm, and it was determined that the model gave lower RMSE values, especially after hyperparameter optimization, compared to other methods. In (Deb, Zhang & Lee, 2017), all machine learning-based methods (SVR, RF, XGBoost, ANN) were compared, and it was found that ensemble methods were more successful than individual models. In (Fazel Zarandi, Hosseini & Turksen, 2020), the ARIMA-XGBoost model was developed using hybrid approaches, and it was stated that both trends and seasonal fluctuations were captured more accurately.

In this study, using Turkey's current 2020-2024 consumption data, the 2025-2030 wind-solar-geothermal energy demand was estimated using ARIMA, Exponential Smoothing, Linear Regression, Artificial Neural Network (MLP), Polynomial Regression, Lasso, Random Forest, Ridge, Support Vector Regression (SVR), and Gradient Boosting (XGBoost) forecasting methods. Post-calculation backtesting was conducted, the models that produced the best results were identified, and the hybrid forecasting method was developed and implemented.

Unlike other studies, this study employed eight different forecasting methods and conducted cross-analysis. A new hybrid model was developed and applied to the same data set, and the results were compared with each forecasting method. A renewable approach is presented by using Türkiye's wind, geothermal, and solar energy consumption as a dataset.

In the study, gross domestic product, population and number of university graduates for the years 2019-2024 were taken into account as independent variables.

The study methodology consisted of data collection and processing into meaningful data, establishing and implementing forecasting models based on the data, validating the forecasts with test data, conducting model performance tests, and determining the hybrid model. In this context, a forecast based on production values was conducted in the study. Data on wind, solar, and geothermal energy consumed in Turkey between 2019 and 2024 were obtained from the Turkish Ministry of Energy and Natural Resources. The data was then processed into meaningful data. The forecast model was created using ARIMA, Exponential Smoothing, Linear Regression, Artificial Neural Network (MLP), Polynomial Regression, Lasso, Random Forest, Ridge, Support Vector Regression (SVR), and Gradient Boosting (XGBoost). The forecast was concluded with retrospective accuracy testing, determining optimal forecasting methods, and creating and implementing a hybrid forecasting system based on these data. Energy consumption data served as the dependent variables in the forecasting studies. The results were analyzed comparatively, and a wind-solar-geothermal energy consumption forecast for 2025-2030 was produced. In the hybrid estimation model, the impact power of the variables affecting the formation of demand was calculated using the Pearson Correlation Statistical method. The flow diagram of the study is shown in Figure 1.

1. Creating the Data Set

Five-year consumption data from the Turkish Ministry of Energy and Natural Resources, covering the years 2019-2024, were analyzed, compiled, and adapted for model use. Total annual consumption data for these resources was obtained based solely on wind, solar, and geothermal energy data.

Figure 2. Real Consumption Values Of Turkey 2020-2024 Geothermal, Solar, And Wind Energy.

Figure 2. Real Consumption Values Of Turkey 2020-2024 Geothermal, Solar, And Wind Energy.

2. Creating and Implementing Forecast Models

The forecasting model was created using ARIMA, Linear Regression, Exponential Smoothing, Polynomial Regression, Random Forest Regressor, XGBoost Regressor, Lasso, Ridge, and SVR forecasting methods on the same dataset.

In the study conducted using ARIMA (AutoRegressive Integrated Moving Average), annual production values were obtained, and trend testing was performed using these values. After selecting the model parameters, the most appropriate p, d, and q values were determined. Forward-looking forecasting was performed using the past 5 years of data. A mathematical equation was created: p: Autoregressive term (AR), d: Differencing number (if there is a trend), q: Moving average (MA), and ϵt: White noise error term. Stationarity Test – ADF Test One of the basic assumptions of the ARIMA model is that the data is stationary. According to the ADF (Augmented Dickey-Fuller) test, the solar production data is not stationary because it contains a trend. It became stationary when the 1st degree difference was taken.

$${\mathrm{Y}}_{\mathrm{t}}^{\prime }=\mathrm{c}+{\mathsf{\phi }}_1·{\mathrm{Y}}_{\mathrm{t}-1}^{\prime }+{\mathsf{\phi }}_2·{\mathrm{Y}}_{\mathrm{t}-2}^{\prime }+{\mathsf{\theta }}_1·{\mathsf{\epsilon }}_{\mathrm{t}-1}^{\prime }+\mathsf{\epsilon }\mathrm{t}$$

(1)

Model Parameter Selection: AR (p), MA (q). To determine these, the ACF (Autocorrelation Function) graph and the PACF (Partial Autocorrelation Function) graph were used. The ACF rapidly decreased to zero after the first delay → the MA component was low, the PACF decayed slowly → the AR component was more significant. Therefore, the most suitable model was found to be ARIMA(2,1,1) according to the AIC criterion. Parameter training was initiated. The trained parameters are shown in Table 1.

The Linear Regression Model is a model that makes future predictions using linear equations. This model performs regression using year information. In this study, the year is expressed as t (e.g., 2020 = 1, 2021 = 2), the learned regression coefficients are expressed as β0-β1, and the error term is expressed as ϵt. β0=8.120, β1=1.32 were taken into account in the calculation. Here, Yt is the dependent variable, t is the independent variable, β0 and β1 are constant values, and ϵt is the error term. The error term is obtained by summing and minimizing the total squared error.

$$\mathrm{Y}\mathrm{ₜ}={\mathsf{\beta }}^0+{\mathsf{\beta }}^1·\mathrm{t}+\mathsf{\epsilon }\mathrm{ₜ}$$

(2)

In the Exponential Smoothing forecasting method, a forecast is made based on a weighted average of historical data. The forecast is made with constant variance, ignoring seasonality and/or trend assumptions. Mathematically, the equation is expressed as x. In the given equation, Yt+1 represents the forecast for period t+1, and the value a represents the smoothing coefficient, which is taken as 0 or 1.

$$\mathrm{Ŷ}{\mathrm{ₜ}}^{+1}=\mathsf{\alpha }·\mathrm{Y}\mathrm{ₜ}+\left(1-\mathsf{\alpha }\right)·\mathrm{Ŷ}\mathrm{ₜ}$$

(3)

The prediction was made using the Polynomial Regression method. Because systems exhibit accelerated growth and decline, the results are highly accurate. In grids containing solar and wind generation, this rate of change is high, and this prediction method is highly accurate. The mathematical model for the polynomial calculation method is shown in equation x. In the study, β0=7.850, β1=1.500, and β2=−35 were included in the calculation.

$$\mathrm{Y}\mathrm{ₜ}={\mathsf{\beta }}^0+{\mathsf{\beta }}^1·\mathrm{t}+{\mathsf{\beta }}^2·{\mathrm{t}}^2+\mathsf{\epsilon }\mathrm{ₜ}$$

(4)

In the case of the prediction using the Random Forest Regressor, the forest model, consisting of the decision tree, was created by preserving only the year values. The mathematical model of the decision trees used in this prediction model is given in equation x. In this equation, Ti represents the ith decision tree, and t represents the year value. Prediction is performed using the relationship between years and rows. In the model, a regression model with 100 trees was created. The trained inputs were 1, 2, 3, 4, and 5. The tree depth was set to 3.

$$\mathrm{Ŷ}\mathrm{ₜ}=(1/\mathrm{N})·\sum \mathrm{ⁿ}\mathrm{ᵢ}₌₁\mathrm{T}\mathrm{ᵢ}\left(\mathrm{t}\right)$$

(5)

In the XGBoost (Boosted Decision Trees) estimation model, decision trees are created as in the Random Forest model, and these decision trees progress by correcting the errors of previous trees. The mathematical model created in this estimation method is shown in equation x. In this equation, fk represents the learned decision trees.

$$\mathrm{Ŷ}\mathrm{ₜ}=\sum _{ k=1}^K\mathrm{f}\mathrm{ₖ}\left(\mathrm{t}\right),\hspace{1em}\mathrm{f}\mathrm{ₖ}\in \mathcal{F}$$

(6)

In the Lasso estimation method, variable selection was made by zeroing the coefficients within the linear structure. Thanks to L1 regularization, variable selection was made by equating some β coefficients to zero, and estimation was made by producing simpler models. In the lasso equation, J(β) represents the model's total loss function (error + penalty). Yᵢ represents the true (observed) value at the ith observation, and Ŷᵢ represents the value predicted by the model. The term (Yᵢ − Ŷᵢ) ² gives the squared error value for each observation, while the sum of these errors indicates the model's fit. βⱼ is the regression coefficient of the jth independent variable. λ (lambda) is the regularization coefficient that determines the model's penalty severity; as it increases, more penalty is applied. |βⱼ| represents the L1 norm, that is, the absolute value of the coefficient. This allows for variable selection by reducing some coefficients to zero. m represents the total number of observations, and n represents the number of independent variables (features) in the model.

$$\mathrm{J}\left(\mathsf{\beta }\right)={\sum _{i=1}^m\left(Yi-\mathrm{Ŷ}\mathrm{ᵢ}\right)}^2+\mathsf{\lambda }\sum _{j=1}^n\left|\mathsf{\beta }\mathrm{ⱼ}\right|$$

(7)

The Ridge estimation method is achieved by adding an L2 penalty to the linear regression model to prevent overfitting. The mathematical model is shown in equation x. In the created model, λ represents the regularization coefficient, and βj represents the model coefficients. In the applied method, the learned parameters were found to be λ = 1.0, β0 = 7.980, and β1 = 1.320. Variables are determined in the model by pushing Bj values to zero. The learned parameters in this model are λ = 0.1, β0 = 8.000, and β1 = 1.310.

$$\mathrm{Ŷ}\mathrm{ₜ}=\mathsf{\beta }₀+\mathsf{\beta }₁·\mathrm{t}+\dots +\mathsf{\beta }\mathrm{ₙ}·\mathrm{t}\mathrm{ⁿ}$$

(8)

$$\mathrm{J}\left(\mathsf{\beta }\right)=\sum \mathrm{ᵐ}(\mathrm{Y}\mathrm{ᵢ}-\mathrm{Ŷ}\mathrm{ᵢ})²+\mathsf{\lambda }\sum \mathrm{ⱼ}₌₁\mathrm{ⁿ}\mathsf{\beta }\mathrm{ⱼ}²$$

(9)

SVR (Support Vector Regression) is an estimation system that eliminates errors outside a certain tolerance without penalizing errors within it. Its mathematical model is shown in equation x. In the given model, C: regularization parameter, ε: tolerance, ξ,ξ∗: error margins. During the training process, c=100 and ε=0.1 were considered.

Backtesting models were trained using data from 2020 to 2023 using a backtesting system. Since 2024 was the actual dataset available, it was used as the test data. Error metrics were calculated by comparing the 2024 forecast data with the actual data. The same process was repeated with 2023 selected as the test year. MAE and RMSE tests were performed. The dataset was divided into chronological order. The data was divided into two groups: training series and test series. In this study, the model was trained between 2019 and 2022. The trained data was tested separately for 2023 and 2024. The accuracy was measured by calculating the error metrics Mean Absolute Error (MAE) and Mean Squared Error (MSE).

$$MAE=(1 / N)\sum ⁿᵢ₌₁ \left|Yᵢ-Ŷᵢ\right|$$

(10)

$$MSE=(1 / N) \sum ⁿᵢ₌₁ (Yᵢ-Ŷᵢ)²$$

(11)

In the calculation, Yₜ → Actual (observed) value, Ŷₜ → Predicted (model output) value, eₜ → Error value (actual value − predicted value), N → Total number of observations (number of t times), Yᵢ → Actual value of the i-th observation, Ŷᵢ → Predicted value of the i-th observation.

3. Pearson Correlation Method

In this study, the effects of variables on the prediction results were statistically determined using the Pearson Correlation Method. The steps of the Pearson Correlation Method were as follows:

• Creating the data set
• Creating the correlation mathematical model
• Calculating the correlation coefficient
• Determining the correlation coefficient and determining the effectiveness levels of their effects on the results
• The Pearson Correlation Mathematical Model is given in Equation x.

$$r=\sum \left(\right(Xİ-Xİ\prime \left)\right(Yİ-Yİ\prime \left)\right)÷\sqrt{\sum \left(\right(Xİ-Xİ\prime \left)\right(Yİ-Y{İ}^{\prime })}$$

(12)

In the given mathematical model;

$Xİ$: each observation value of the independent variable (for example: GDP)

$Yİ$: each observation value of the dependent variable (Electricity Consumption)

$Xİ\prime$ $Y{İ}^{\prime } :$the mean of each variable

r: correlation coefficient

Correlation analysis:

r=+1; perfect positive correlation

r=-1; perfect negative correlation

r=0; No correlation

Correlation Coefficient (r)	Relationship Type
+0.90 ~ +1.00	Very strong positive relationship
+0.70 ~ +0.89	Strong positive relationship
+0.50 ~ +0.69	Moderate positive correlation
+0.30 ~ +0.49	Weak positive correlation
0	No relationship
-0.30 ~ -1.00	Negative (inverse) relationship