Mariano Test Research Articles

Testing for Equal Average Forecast Accuracy in Possibly Unstable Environments *

We consider the issue of testing the null of equal average forecast accuracy in a model where the forecast error loss differential series has a potentially non-constant mean function over time. We show that when time variation is present in the loss differential mean, the standard Diebold and Mariano (1995) test, which was proposed for evaluating forecasts in a stable environment, has an asymptotic size of zero, and, whilst consistent, can have reduced local power. This arises due to inconsistent estimation of the implicit long run variance estimator, which diverges under a time varying mean. We suggest a modified statistic that replaces the standard long run variance estimator based on full-sample demeaning of the loss differential series with one based on nonparametric local demeaning. The new long run variance estimator is consistent under both the null and alternative when the mean function is time varying or constant, and in both cases, the modified test recovers the asymptotic size and power properties associated with the original test in the constant mean case. The modified test therefore provides a robust method for testing the equal average forecast accuracy null, allowing for instability in the loss differential mean. The benefits of our test are demonstrated via Monte Carlo simulation and two empirical applications.

Forecasting Orange Juice Futures: LSTM, ConvLSTM, and Traditional Models Across Trading Horizons

This study evaluated the forecasting accuracy of various models over 5-day and 10-day trading horizons to predict the prices of orange juice futures (OJ = F). The analysis included traditional models like Autoregressive Integrated Moving Average (ARIMA) and advanced neural network models such as Long Short-Term Memory (LSTM), Recurrent Neural Network (RNN), Backpropagation Neural Network (BPNN), Support Vector Regression (SVR), and Convolutional Long Short-Term Memory (ConvLSTM), incorporating factors like the Commodities Index and the S&P500 Index. We employed loss function metrics and various tests to assess model performance. The results indicated that for the 5-day horizon, the LSTM and ConvLSTM consistently outperformed the other models. LSTM achieved the lowest error rates and demonstrated superior capability in capturing temporal dependencies, especially in single-factor and S&P500 Index predictions. ConvLSTM also performed strongly, effectively modeling spatial and temporal data patterns. In the 10-day horizon, similar trends were observed. LSTM and ConvLSTM models had significantly lower errors and better alignment with actual values. The BPNN model performed well when all factors were included, and the SVR model maintained consistent accuracy, particularly for single-factor predictions. The Diebold–Mariano (DM) test indicated significant differences in forecasting accuracy, favoring advanced neural network models. In addition, incorporating multiple influencing factors further improved predictive performance, enhancing investment outcomes and reducing risk.

Asymmetric impact of energy prices on financial cycles based on interval time series modeling

Energy prices crucially affect financial cycles. We employ the bivariate empirical mode decomposition (BEMD) model to disaggregate the daily interval data of the volatility index (VIX) and rely on the threshold autoregressive interval model (TARI) to incorporate energy prices into the forecasting model. Furthermore, the threshold interval decomposition ensemble (TIDE) is used to forecast the VIX series with nonlinearities to improve the forecasting accuracy. Moreover, we apply the root mean square error (RMSE) and the Diebold–Mariano test (DM) to evaluate the TIDE model performance across various frequency components and the final integration results. This paper demonstrates a significant correlation between energy prices and financial cycles, along with a temporal asymmetry effect. While the impact of energy prices on improving VIX forecasting is minimal in the short term, it becomes substantial over medium and long terms. Specifically, the influence of liquefied petroleum gas (LPG) prices on the VIX is notable in both medium and long terms. Our results offer new insights and methodologies for predicting financial cycles, assisting investors in evaluating volatility-related exchange-traded products. Additionally, these findings are crucial for developing more effective policies to promote green energy development.

Evaluating Volatility Using an ANFIS Model for Financial Time Series Prediction

This paper develops and implements an Autoregressive Integrated Moving Average model with an Adaptive Neuro-Fuzzy Inference System (ARIMA-ANFIS) for BTCUSD price prediction and risk assessment. The goal of these forecasts is to identify patterns from past data and achieve an understanding of the future behavior of the price and its volatility. The proposed ARIMA-ANFIS model is compared with a benchmark ARIMA-GARCH model. To evaluated the adequacy of the models in terms of risk assessment, we compare the confidence intervals of the price and accuracy measures for the testing sample. Additionally, we implement the diebold and Mariano test to compare the accuracy of the two volatility forecasts. The results revealed that each volatility model focuses on different aspects of the data dynamics. The ANFIS model, while effective in certain scenarios, may expose one to unexpected risks due to its underestimation of volatility during turbulent periods. On the other hand, the GARCH(1,1) model, by producing higher volatility estimates, may lead to excessive caution, potentially reducing returns.

Efficient prediction for Blast Furnace Gas holder level using novel preprocessing techniques and weight correction strategy

Accurately forecasting the level of Blast Furnace Gas (BFG) holder, managing the balance of gas supply and demand, strategically allocating BFG brings substantial economic and social benefits. In order to address the issues of volatile fluctuation, strong temporal variability, and high uncertainty of BFG, this paper proposes an efficient system for predicting the BFG holder level. Variational Mode Decomposition is utilized to separate components with different frequencies. The number of modes is determined according to Energy Ratio. Improved Discrete Wavelet Threshold is employed to eliminate noise. The grid search approach adjusts the activation functions. What is more, Particle Swarm Optimization is used to correct the weights of subsequences and emphasize critical information. Experimental results demonstrate that Root Mean Squared Error of the system are 0.0411, 0.0423 and 0.0416 for the three real-time monitoring datasets in April 2021. The average improvement percentage for the second dataset is 67.5% when compared to other commonly models. It is obvious that the prediction errors are minimized, and the stability and generalizability of the hybrid prediction system are enhanced. Additionally, the performance of the system is further verified through Diebold–Mariano test, improvement percentage test, and effectiveness test.

The application of fractional calculus in economic growth modelling: An approach based on regression analysis

This paper establishes a fractional-order economic growth model to model the gross domestic product (GDP). The fractional-order model consists of a differential equation of integer and fractional orders, where the GDP is a function of several exploratory variables. An empirical application is adopted using Malaysia's GDP data from 1956 to 2018, incorporating exploratory variables such as total population, crude death rate, production of logs, gross fixed capital formation, exports of goods and services, general government final consumption expenditure, private final consumption expenditure, and the impact of investment. Extensive comparisons were carried out to evaluate the modelling performance of the full and reduced fractional-order multiple linear regression models with the benchmark models, namely full and reduced integer-order multiple linear regression models. Results indicate that the reduced fractional-order model with six exploratory variables, excluding the crude death rate and production of logs, predominates other models for the in-sample model fitting based on the Akaike information criterion, coefficient of determination and other criteria. Furthermore, the fractional-order model offers the best-of-sample forecasts evaluated based on the root mean square forecast error and mean absolute forecast error. The application of the Diebold–Mariano test also serves to confirm the superior performance of the suggested fractional-order model, revealing a significant difference in forecasting ability between the fractional-order and integer-order models.

Enhanced multi-step streamflow series forecasting using hybrid signal decomposition and optimized reservoir computing models

This study evaluates the use of different time series decomposition methods in association with echo state networks (ESNs), deep echo state networks (DeepESNs), and next generation reservoir computing (NGRC) models to predict the natural flow of water in two hydropower reservoirs with horizons of one, seven, fourteen, and twenty-one steps ahead. The Coyote optimization algorithm is used to adjust the hyperparameters of the ESNs. The use of reservoir computing (RC) methods with Coyote optimization algorithm, a swarm intelligence approach, is compared with the use of variational mode decomposition (VMD), empirical wavelet transform, and empirical mode decomposition. Analysis of the results shows that the use of signal decomposition methods in association with RC can improve the accuracy and performance of the prediction model. The results are compared using different statistical metrics, showing that, in most cases, decomposition methods can improve the forecasting performance of RC. Overall, NGRC outperformed ESN and DeepESN in most of evaluated cases. The best results were obtained using VMD for the forecast horizons of 7, 14, and 21 days ahead, with a decrease in mean absolute error in a range from 43.70% to 88.88% compared to all the other models. Using a Diebold–Mariano test, the results show that the use of VMD is statistically significant in all the cases, with a significant value of 1% in all tested cases of ESN forecasting.

Joint Component Estimation for Electricity Price Forecasting Using Functional Models

This work considers the issue of modeling and forecasting electricity prices within the functional time series approach. As this is often performed by estimating and predicting the different components of the price dynamics, we study whether jointly modeling the components, able to account for their inter-relations, could improve prediction with respect to a separate instance of modeling. To investigate this issue, we consider and compare the predictive performance of four different predictors. The first two, namely Smoothing Splines-Seasonal Autoregressive (SS-SAR) and Smoothing Splines-Functional Autoregressive (SS-FAR) are based on separate modeling while the third one is derived from a single-step procedure that jointly estimates all the components by suitably including exogenous variables. It is called Functional Autoregressive with eXogenous variables (FARX) model. The fourth one is a combination of the SS-FAR and FARX predictors. The predictive performances of the models are tested using electricity price data from the northern zone of the Italian electricity market (IPEX), both in terms of forecasting error indicators (MAE, MAPE and RMSE) and by means of the Diebold and Mariano test. The results point out that jointly estimating the components leads to significantly more accurate predictions than using a separate instance of modeling. In particular, the MAE, MAPE, and RMSE values for the best predictor, based on the FARX(3,0,4) model, are 4.25, 9.28, and 5.38, respectively. The percentage error reduction is about 20% with respect to SS-SAR(3,1) and about 10% with respect to SS-FAR(5). Finally, this study suggests that the forecasting errors are generally higher on Sunday and Monday, from hours 3 to 6 in the morning and 14 to 15 in the afternoon, and in June and December. On the other hand, prices are relatively lower on Wednesday, Thursday, and Friday, from hour 20 to 1 a.m., and in January and February.

Solar photovoltaic power forecasting system with online manner based on adaptive mode decomposition and multi-objective optimization

Constructing an accurate and reliable solar photovoltaic (PV) power forecasting system is crucial for smart grid management and dispatch. However, due to the intermittent, non-stationary and random nature of solar energy, current methods cannot effectively capture the dynamic change patterns of PV data, resulting in a forecasting accuracy that cannot satisfy the requirement for stable operation of smart grids. To address this issue, in this paper, a new solar PV power forecasting system is proposed based on a new adaptive mode decomposition method that combines machine learning models. First an adaptive mode decomposition method is proposed for adaptively eliminating high-frequency information of PV data, mitigating the impact of high noise on the forecasting performance. Then the powerful mapping ability of machine learning model is utilized to construct a solar PV power generation combination forecasting system. The system adopts a multi-objective optimization strategy to determine the optimal weights of the combination model, which reduces the volatility of the forecasting results and enhances the stability of the forecasting system. Experimental results demonstrate that the proposed system achieves the best overall performance with online manner on 10 state-of-the-art baselines. Furthermore, the evaluation analysis by Diebold–Mariano test, improvement ratio and sensitivity analysis further show that the stability and accuracy of the proposed system outperforms the comparative baselines.

Deep Learning Wind Power Prediction Model Based on Attention Mechanism-Based Convolutional Neural Network and Gated Recurrent Unit Neural Network

Accurate prediction of wind power is crucial for the efficient operation and risk management of wind farms. This paper introduces a deep learning model for wind power prediction that integrates an Attention mechanism with a convolutional neural network (CNN) and a gated recurrent unit (GRU) neural network. Addressing the randomness, intermittency, volatility and uncertainty of wind speed, we first apply swarm decomposition (SWD) to preprocess the original wind power data into subsequences. Subsequently, the CNN extracts spatial features, and the GRU identifies temporal correlations. The Attention mechanism enhances feature significance, further optimizing prediction accuracy. Complex error sequences generated by the CNN–GRU–Attention (CGA) model are corrected using the autoregressive integrated moving average (ARIMA). We evaluated the model’s performance using three wind power datasets against 16 other models, employing six evaluation indices (MSE, RMSE, MAPE, Theil’s [Formula: see text], TIC and SPL) and the Diebold–Mariano (DM) test and model confidence set (MCS) for model testing. Our results demonstrate the proposed model’s superior accuracy and efficiency in predicting wind power.

A Hybrid Model for Carbon Price Forecasting Based on Improved Feature Extraction and Non-Linear Integration

Accurately predicting the price of carbon is an effective way of ensuring the stability of the carbon trading market and reducing carbon emissions. Aiming at the non-smooth and non-linear characteristics of carbon price, this paper proposes a novel hybrid prediction model based on improved feature extraction and non-linear integration, which is built on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), fuzzy entropy (FuzzyEn), improved random forest using particle swarm optimisation (PSORF), extreme learning machine (ELM), long short-term memory (LSTM), non-linear integration based on multiple linear regression (MLR) and random forest (MLRRF), and error correction with the autoregressive integrated moving average model (ARIMA), named CEEMDAN-FuzzyEn-PSORF-ELM-LSTM-MLRRF-ARIMA. Firstly, CEEMDAN is combined with FuzzyEn in the feature selection process to improve extraction efficiency and reliability. Secondly, at the critical prediction stage, PSORF, ELM, and LSTM are selected to predict high, medium, and low complexity sequences, respectively. Thirdly, the reconstructed sequences are assembled by applying MLRRF, which can effectively improve the prediction accuracy and generalisation ability. Finally, error correction is conducted using ARIMA to obtain the final forecasting results, and the Diebold–Mariano test (DM test) is introduced for a comprehensive evaluation of the models. With respect to carbon prices in the pilot regions of Shenzhen and Hubei, the results indicate that the proposed model has higher prediction accuracy and robustness. The main contributions of this paper are the improved feature extraction and the innovative combination of multiple linear regression and random forests into a non-linear integrated framework for carbon price forecasting. However, further optimisation is still a work in progress.

Tests for equal forecast accuracy under heteroskedasticity

SummaryHeteroskedasticity is a common feature in empirical time series analysis, and in this paper, we consider the effects of heteroskedasticity on statistical tests for equal forecast accuracy. In such a context, we propose two new Diebold–Mariano‐type tests for equal accuracy that employ nonparametric estimation of the loss differential variance function. We demonstrate that these tests have the potential to achieve power improvements relative to the original Diebold–Mariano test in the presence of heteroskedasticity, for a quite general class of loss differential series. The size validity and potential power superiority of our new tests are studied theoretically and in Monte Carlo simulations. We apply our new tests to competing forecasts of changes in the dollar/sterling exchange rate and find the new tests provide greater evidence of differences in forecast accuracy than the original Diebold–Mariano test, illustrating the value of these new procedures for practitioners.

Hidden Markov guided Deep Learning models for forecasting highly volatile agricultural commodity prices

Predicting agricultural commodity prices accurately is of utmost importance due to various factors such as perishability, seasonality, production uncertainty etc. Moreover, the substantial volatility that may be exhibited in time series further adds to the complexity and constitutes a significant challenge. In this paper, a Hidden Markov (HM) guided Deep Learning (DL) models has been developed on nonlinear and nonstationary price data of agricultural commodities for forecasting by considering technical indicators viz., Moving Average (MA), Bollinger Bands (BB), Moving Average Convergence Divergence (MACD), Exponential MA (EMA) and Fast Fourier Transformation (FFT). HM Models (HMMs) can effectively handle the sequential dependencies and hidden states, while DL approach can learn complex patterns and relationships within the price series and thus the drawback of lack of generalization capability in the DL model has been overcome by HMM. In this study, the Potato price data of the Champadanga district of West Bengal, India has been utilized to assess the performance of the proposed technique. HMM has been combined with six baseline DL models viz., Recurrent Neural Networks (RNN), Convolutional Neural Networks (CNN), Long Short-Term Memory (LSTM), Gated Recurrent Units (GRU), Bidirectional LSTM (BiLSTM) and Bidirectional GRU (BiGRU) for forecast modeling. Performance evaluation metrics viz., Root Mean Squared Error (RMSE), Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE) and the insightful Diebold–Mariano (DM) test revealed that Hidden Markov hybridized with DL models surpassed baseline DL models in forecasting accuracy for 1-week, 4-week, 8-week and 12-week ahead DL predictions. The proposed approach holds significant promise for enhancing the precision of agricultural commodity price forecasting with far-reaching implications for various stakeholders such as farmers and planners.

Evaluation of forecasting models for improved passenger market management and rolling stock planning on Indian railways

Purpose Indian railways (IR) is one of the largest railway networks in the world. As a part of its strategic development initiative, demand forecasting can be one of the indispensable activities, as it may provide basic inputs for planning and control of various activities such as coach production, planning new trains, coach augmentation and quota redistribution. The purpose of this study is to suggest an approach to demand forecasting for IR management. Design/methodology/approach A case study is carried out, wherein several models i.e. automated autoregressive integrated moving average (auto-ARIMA), trigonometric regressors (TBATS), Holt–Winters additive model, Holt–Winters multiplicative model, simple exponential smoothing and simple moving average methods have been tested. As per requirements of IR management, the adopted research methodology is predominantly discursive, and the passenger reservation patterns over a five-year period covering a most representative train service for the past five years have been employed. The relative error matrix and the Akaike information criterion have been used to compare the performance of various models. The Diebold–Mariano test was conducted to examine the accuracy of models. Findings The coach production strategy has been proposed on the most suitable auto-ARIMA model. Around 6,000 railway coaches per year have been produced in the past 3 years by IR. As per the coach production plan for the year 2023–2024, a tentative 6551 coaches of various types have been planned for production. The insights gained from this paper may facilitate need-based coach manufacturing and optimum utilization of the inventory. Originality/value This study contributes to the literature on rail ticket demand forecasting and adds value to the process of rolling stock management. The proposed model can be a comprehensive decision-making tool to plan for new train services and assess the rolling stock production requirement on any railway system. The analysis may help in making demand predictions for the busy season, and the management can make important decisions about the pricing of services.

Nowcasting the Russian economy macroeconomic indicators under uncertainty: Does taking into account the news sentiment help?

In this paper the following models are compared: restricted and unrestricted MIDAS-models (mixed data sampling models), MFBVAR-model (mixed frequency Bayesian vector autoregression), Linear model with regularization (MIDAS_L1-, MIDAS_L2and MIDAS_PC-model) and dynamic factor model. The results are compared with classical autoregression as a benchmark. Production indices for different industries and indicators characterizing Russian GDP and its components, energy prices and PMI of Russia and its main trading partners, as well as indicators derived from the analysis of sentiment of news articles published by a number of major media and blogs are used as explanatory variables. The paper also proposes a method of rapid assessment of the current state of the economy based on data for the first or first two months of the quarter in question only. The use of this approach in combination with news sentiment analysis allows to draw conclusions about current economic situation extremely rapidly. Models’ accuracy is assessed by cross-validation for periods before and after the Q2 2022, the significance of the effect of adding news variables is assessed using the Diebold—Mariano test. When testing during the crisis period (starting from the Q1 2022), the addition of news variables leads to an increase in accuracy for 45% of the models considered, and the average improvement (reduction in the average absolute error) was 1.39 points (the reduction in MAE for the science-based GDP growth rates of Russia is 0.64 p.p.). At the same time, in a calmer (pre-sanction) period, the advantage of news is less noticeable: an increase in accuracy was recorded in 30% of cases with an average decrease in error of 1.54 points (the decrease in MAE for Russia’s GDP growth rate is 0.26 p.p.), and the change accuracy of science data when adding variables reflecting the news background turns out to be statistically insignificant. Thus, the use of news sentiment is not a “silver bullet” in the task of nowcasting Russian GDP, but in times of crisis it can serve as a good and, importantly, very operative indicator of the state of the economy and can be used in conjunction with more traditional explanatory variables.

An optimized deep learning approach for forecasting day-ahead electricity prices

Electricity price forecasting is essential for reliable and cost-effective operations in the power industry. However, the complex and nonlinear structure of the electricity price series presents uncertainties and challenges for energy management. To address this, artificial intelligence models such as SARIMAX, LSTM, and CNN-LSTM have been developed to predict short-term electricity prices. These models were tested using Mean Absolute Error, Root-Mean Squared Error, Mean Absolute Percentage Error, and percentage accuracy to verify their accuracy and to compare forecasting methodologies. The study includes the Diebold–Mariano test to confirm the statistical significance of the difference between the forecast errors of the two models. Ensemble learning was used to optimize a CNN-LSTM model, which automatically selects the best model by using CNN to extract valuable characteristics and LSTM to recognize data dependency in time series. Historical data from the German electrical market were used to validate the models’ prediction performance. The results showed that the LSTM and CNN-LSTM models outperformed the SARIMAX model in terms of accuracy and simplicity, with the CNN-LSTM technique having significant forecasting advantages. These methods can be used for intelligent optimization forecasting of electricity prices.

A hybrid crude oil price forecasting framework: Modified ensemble empirical mode decomposition and hidden Markov regression

AbstractThe considerable influence of crude oil prices on the international economy has motivated numerous scholars to develop various prediction models. Two difficulties are encountered in forecasting. One is that the time series of crude oil prices show massive jumps in high frequency. The other is that the time series of crude oil prices are characterised by nonlinearity, structural breaks and highly volatile states. Therefore, we propose a hybrid model that incorporates the principle of decomposition–integration. Its overall process can be divided into the steps of decomposition and integration. In decomposition step, modified ensemble empirical mode decomposition is used to decompose the data on crude oil prices. Next, K‐means and principal component analysis are utilised to extract the optimal intrinsic mode function (IMF) from diverse frequencies amongst decomposed IMFs. Following decomposition, different forecasting methods are used to match IMFs with various frequencies for prediction. In accordance with structural breaks and the highly volatile states of high‐frequency series, hidden Markov regression is applied to describe predicted values in a probabilistic manner, providing objective interpretation and forecasting. A neural network is taken to predict intermediate‐frequency IMFs by using a fully connected network. Owing to the low frequency and tendency of the residual sequence to be more stable than other frequency sequences, the autoregressive integrated moving average model is applied as the forecasting method for prediction. Finally, all individual predictions for the eventual results are ensembled as final predictions. Results confirm that the proposed model is better than several normal hybrid and single models in terms of prediction accuracy and Diebold–Mariano test results. All results confirm that the newly proposed hybrid model is a promising tool for the analysis and forecasting of crude oil prices.

Regime-dependent 1-min irradiance separation model with climatology clustering

Since directly measuring beam and diffuse irradiance is not feasible on many occasions, one often has to resort to estimating the beam and diffuse irradiance components from the global irradiance, which is known as separation modeling. Separation modeling is essentially a nonlinear regression problem, with the clearness index being the main input and the diffuse fraction being the output. Hundreds of separation models with various complexities have been proposed, among which the Yang4 model was recently validated using worldwide data as the quasi-universal choice for 1-min data. In this work, Yang4 is further improved by regime-dependent fitting, i.e., fitting a separate set of model coefficients for each climatological regime. Different regimes are determined through clustering of cloud cover frequency, aerosol optical depth, and surface albedo climatology maps. The new Yang5 model is able to outperform its predecessor at the 126 stations tested, covering a wide range of climate types. Overall, the normalized root mean square errors for beam normal irradiance (BNI) and diffuse horizontal irradiance (DHI) of Yang5 are 17.55% and 32.92% on average, as compared to 19.13% and 34.94% for the next best model, namely, Yang4. Furthermore, through conducting pairwise Diebold–Mariano tests, Yang5 is shown superior to Yang4 at 110/126 sites for BNI prediction and 93/126 for DHI.

A hybrid EMD-GRNN-PSO in intermittent time-series data for dengue fever forecasting

Accurate forecasting of dengue cases number is urgently needed as an early warning system to prevent future outbreaks. However, forecasting dengue fever cases with intermittent data characteristics are still rare. In addition, good forecasting accuracy for intermittent data is also challenging to obtain. A hybrid Empirical Mode Decomposition (EMD), Generalized Regression Neural Network (GRNN), and Particle Swarm Optimization (PSO) were proposed to solve the problem. First, data preprocessing is done to ensure that the data is ready for further processing and has a relationship with the dengue fever case number. Second, the decomposition extracts the non-stationarity and nonlinearity patterns of each predictor variable and transforms them into several intrinsic mode functions (IMFs). Third, using various data training and testing ratios and cross-validation, the IMFs of each predictor variable were trained with GRNN to capture the best model of dengue fever cases forecasting. PSO algorithm is used to find the optimal parameters of GRNN so that the parameter searching process is more efficient and accuracy increases. Finally, to see the robustness and effectiveness of the proposed hybrid approach, the forecasting performance of the proposed hybrid model was assessed on 21 datasets with different intermittent conditions, data periods, geographical conditions, diverse numbers, and ranges of data. This approach also compared the comparative benchmark models, using MSE, MAE, and SMAPE as evaluation indicators. The Diebold–Mariano test and the pairwise sample t-test show that the proposed model is more reliable in handling intermittent data.

Time Series Forecasting for Energy Production in Stand-Alone and Tracking Photovoltaic Systems Based on Historical Measurement Data

This article presents a time series analysis for predicting energy production in photovoltaic (PV) power plant systems, namely fixed and solar-tracking ones, which were located in the north-east of Poland. The purpose of one-day forecasts is to determine the effectiveness of preventive actions and manage power systems effectively. The impact of climate variables affecting the production of electricity in the photovoltaic systems was analyzed. Forecasting models based on traditional machine learning (ML) techniques and multi-layer perceptron (MLP) neural networks were created without using solar irradiance as an input feature to the model. In addition, a few metrics were selected to determine the quality of the forecasts. The preparation of the dataset for constructing the forecasting models was discussed, and some ways for improving the metrics were given. Furthermore, comparative analyses were performed, which showed that the MLP neural networks used in the regression problem provided better results than the MLP classifier models. The Diebold–Mariano (DM) test was applied in this study to distinguish the significant differences in the forecasting accuracy between the individual models. Compared to KNN (k-nearest neighbors) or ARIMA models, the best results were obtained for the simple linear regression, MLPRegressor, and CatBoostRegressor models in each of the investigated photovoltaic systems. The R-squared value for the MLPRegressor model was around 0.6, and it exceeded 0.8 when the dataset was split and separated into months.