3.1. Analysis of Trends in Energy Efficiency Developments
The efficacy of energy efficiency strategies in various sectors is corroborated by the OLS regression results, as depicted in
Figure 1. The regression outcomes for each sector—industry, transport, households, and overall—furnish empirical proof of year-to-year fluctuations in the ODEX index. The results of the linear regression for the industrial sector demonstrate a high coefficient of determination
of 0.988, indicating a strong fit between the model and the historical data. The
p-value for the year variable is less than 0.05, indicating that it is statistically significant in the model. The regression coefficient for the year is −0.6109, indicating that, on average, industrial energy efficiency increases (ODEX decreases) by 0.6109 points for each year.
Analyses conducted for transport, households and the general public also demonstrated statistically significant negative regression coefficients, indicating improvements in energy efficiency in these sectors.
Analysing the ODEX indicator data for Poland between 2011 and 2021, it is evident that there have been clear trends in energy efficiency in different sectors of the economy. The industrial sector demonstrates a consistent decline in the indicator, from 52.1 in 2011 to 45.7 in 2021, indicating a notable improvement in efficiency by over 6 percentage points. This positive change can be attributed to the implementation of modern technologies, the optimisation of production processes and investments in energy-efficient solutions.
In the transport sector, the ODEX index also demonstrates a decline, from 92.5 in 2011 to 84.6 in 2021. This suggests that energy efficiency in transport is improving, potentially due to the modernisation of vehicle fleets and the promotion of clean transport modes.
The household sector also exhibits an enhancement in efficiency, from 85.4 in 2011 to 75.9 in 2021. The reduction in the value of the indicator in this sector can be attributed to improvements in thermal insulation of buildings, the implementation of more efficient heating systems and an increase in consumer energy awareness.
Overall, the ODEX indicator for total energy consumption in Poland has decreased from 77.5 in 2011 to 70.7 in 2021, indicating an overall improvement in the country’s energy efficiency. Nevertheless, it is essential to acknowledge that each year brings a distinctive set of challenges and circumstances that may have influenced these outcomes, including alterations in the economy, energy policy, energy commodity prices or the implementation of new regulations.
It should be noted, however, that these analyses are limited by the small number of observations (n = 11 years of data), which may affect the stability of the estimation and interpretation of statistical tests such as the Omnibus or Jarque–Bera test. These tests are more reliable with a larger number of observations. Furthermore, high conditional number values may indicate the potential for multicollinearity in the data. However, this is unlikely in the context of a simple linear model with one independent variable.
3.3. The Hypothesis Testing
Statistical hypothesis testing represents a pivotal step in scientific research, serving to verify whether observed results are statistically significant or may be the result of random variation. The fundamental concepts at play are the null hypothesis (H0) and the alternative hypothesis (H1). The null hypothesis represents an initial assumption about the data, typically indicating the absence of an effect or difference. The alternative hypothesis is the hypothesis that is accepted when the null hypothesis is rejected. The following hypotheses have been formulated:
Null hypothesis (H0): It can be concluded that there is no statistically significant change in energy efficiency over the period analysed.
Conversely, there is a statistically significant change in energy efficiency over the period analysed.
This is the standard approach used when investigating whether the observed data differs from a particular value. The following equation was employed:
t is the value of the t-test statistic;
is the average observed in the sample;
is the reference value against which we compare the average;
s is the standard deviation of the sample;
n is the number of observations in the sample.
The statistical significance of the changes in energy efficiency within each sector was confirmed through
t-test analysis. The results, presented in
Table 2, demonstrate that all sectors—industry, transport, households, and the aggregate total—have exhibited statistically significant improvements in energy efficiency over the period studied.
One-sample t-tests for the ODEX indicators revealed that the mean values of the indicators from 2011 to 2021 are statistically distinct from the 2000 baseline. The p-value is considerably less than the standard significance level of 0.05, thereby allowing the null hypothesis (H0) to be rejected. These findings thus indicate a notable enhancement in energy efficiency across the analysed sectors in comparison to the base year.
Analyses and comparisons of the energy efficiency of individual economic sectors with the aggregate for the country as a whole are a key element in understanding the dynamics of energy consumption and identifying potential areas for improvement. Such analysis provides valuable insights for policy makers, economic decision makers and researchers, enabling a better understanding of how individual sectors contribute to the overall energy balance of the country. The results of the statistical tests and associated p-values for comparing the ‘Industry’, ‘Transport’ and ‘Households’ sectors with the ‘Total’ aggregate are presented below.
Given the limitations associated with the normality of the distribution for the ‘Transport’ sector, the use of the traditional
t-test for independent samples may not be appropriate. Consequently, an alternative statistical method was employed, namely the Mann–Whitney U test (also known as the Wilcoxon test for two independent samples). This is a non-parametric test used to compare two independent groups. Unlike parametric tests, it does not require an assumption of normality of distribution and can be used to assess whether two independent samples come from the same distributions. The selection of an appropriate method is contingent upon the nature of the data, the objective of the analysis and the specific assumptions inherent to the study in question. In the context of the available data, given that the assumption is to compare a sector with the aggregate ‘Total’ in order to ascertain the degree to which household energy efficiency differs from the total energy efficiency of all sectors, the Mann–Whitney U test may be a suitable method to assess the significance of these differences without assuming normality of distribution. The following equation was employed:
In order to assess the differences in energy efficiency between individual sectors and the economy as a whole, the Mann-Whitney U-test was applied, as demonstrated in
Table 3.
A comparison of the results presented in the table above reveals statistically significant differences between the various sectors and the aggregate ‘Total’. This indicates a notable divergence in energy efficiency between the sectors under analysis and the wider economy. The test statistic provides further insight into the relationship between the ranks of the compared groups and the low p-values confirm the significance of these differences. Nevertheless, the values of the test statistic exhibit discrepancies, which provide insights into the nature of these differences and their potential significance. These insights will be presented in the subsequent section of the article, the discussion.
In the context of the analyses comparing the energy efficiency of different economic sectors (namely, ‘Industry’, ‘Transport’ and ‘Households’) with the aggregate ‘Total’ using the Mann–Whitney U test, a key objective was to test two hypotheses for each sector.
The null hypothesis (H0) states that there is no statistically significant difference in energy efficiency between the sector and the aggregate ‘Total’.
The alternative hypothesis (H1) states that there is a statistically significant difference in energy efficiency between the sector and the aggregate ‘Total’. The results of the statistical tests indicate that there is a statistically significant difference in energy efficiency between the sector and the aggregate ‘Total’. All tests carried out result in the rejection of the null hypotheses (low p-value), which implies that for each of the sectors analysed, there are statistically significant differences in energy efficiency compared to the average energy efficiency at an economy-wide level. This indicates that the ‘Industry’, ‘Transport’ and ‘Households’ sectors exhibit characteristics that diverge from the prevailing trend, necessitating the implementation of targeted measures to enhance energy efficiency in these domains.
3.4. Future Energy Efficiency Trends
The historical analysis of the ODEX indicator has revealed patterns and trends that are essential to evaluating past efforts to improve energy efficiency. However, as we stand on the threshold of significant environmental and technological change, it becomes increasingly important to look ahead, projecting these trends for years to come. This forward-looking analysis not only anticipates the challenges and opportunities that lie ahead, but also serves as a guide for strategic planning and policy formulation to achieve a more energy-efficient and sustainable future.
In modelling and forecasting the Operational Energy Efficiency Index (ODEX) for different economic sectors, it is important to use a methodology that strikes a balance between model accuracy and understandability. The decision to choose a simplified first-order autoregressive model (AR1) is based on several key considerations that translate into the reliability and practical value of the analyses performed. These include:
The effectiveness of this approach in capturing temporal relationships is particularly useful for the ODEX indicator, where past values can be strong predictors of future trends.
The simplicity and interpretability of this model are also noteworthy. In comparison to more complex models such as ARIMA, this model is characterised by greater interpretability. This is evidenced by the fact that while the AR component was significant, the MA component no longer made a significant contribution to the model.
Practical verifiability: This allows for easier verification and comparison of results with available historical data and future observations. This is important for ongoing monitoring of the effectiveness of energy policies and identifying areas for intervention.
The following equation was employed:
represents the value of the variable at time t;
is a constant;
is the autoregression coefficient, which indicates the extent to which the previous value
represents the value of the variable at time t − 1;
is the random error (noise) at time t, assuming that ), i.e., it has a normal distribution with mean equal to 0 and variance .
The parameter values and are estimated on the basis of historical data.
The data presented in
Table 4 indicates a discernible, albeit slight, increase in the ODEX indicator across all sectors between the years 2025–2027. This may suggest a gradual reduction in energy efficiency and an increase in energy use in relation to sectoral activity. The overall upward trend in the ODEX indicator points to potential challenges in improving energy efficiency at an economy-wide level.
An assessment of the fit of the AR1 models for all sectors was also carried out, with a focus on the diagnostic statistics of the model residuals using the Ljung–Box test. This analysis verified that the residuals from the model are close to a normal distribution and do not show autocorrelation, which could indicate an inappropriate model fit. In addition, the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) values were evaluated to assess the overall quality of the model.
One of the fundamental aspects of regression analysis is the examination of residuals, which serves to ensure the model’s adequacy. The residual analysis for the industrial sector, which encompasses an investigation of the distribution of residuals and their autocorrelation, is depicted in
Figure 4.
The histogram of the residuals analysis for the industrial sector displays a distribution that is close to normal. Additionally, the autocorrelation plot indicates that there is no significant autocorrelation, which suggests that the AR1 model is adequately fitted to the data in this sector.
In our assessment of model diagnostics for the household sector, we examined the distribution of residuals and their autocorrelations to ascertain whether there were any deviations from the assumed model conditions. The findings of this analysis are illustrated in
Figure 5.
The residual analysis for the household sector also indicates a distribution that is close to normal. Furthermore, the autocorrelation plot shows no evidence of autocorrelation problems, which suggests that the AR1 model is effective in this context.
A residual analysis was also conducted on the regression model for the transport sector.
Figure 6 presents the residuals histogram and autocorrelation plot for this sector.
Similarly, the histogram of the residuals exhibits a near-normal distribution and the absence of significant peaks in the autocorrelation plot indicates that the AR1 model is performing well with the data. The comprehensive assessment of our regression model also includes an evaluation of the residuals for the aggregated data across all sectors.
Figure 7 illustrates the residuals histogram and autocorrelation plot for the total dataset, which allows us to verify the normality of residuals and the assumption of no autocorrelation.
The results are comparable to those observed in other sectors, with a histogram indicating the normality of the residual distribution and an autocorrelation plot demonstrating the absence of significant autocorrelation in the residuals.
The residual histograms for all sectors appear to be close to a normal distribution, which is a positive indicator. The autocorrelation plots do not indicate the presence of significant autocorrelation in the residuals, suggesting that the models effectively incorporate the information contained in the data.
The Ljung–Box test is a statistical test used to assess the presence of significant autocorrelations in the time series or model residuals at a given lag level. This test is particularly useful in the context of time series modelling, where it is important that the model residuals (errors) are white noise, i.e., show no autocorrelation. This test helps to verify whether the model adequately explains the data, or whether there are additional patterns that the model does not capture. The test statistic Q in the Ljung–Box test is calculated as:
n is the number of observations;
h is the number of delays taken into account in the test;
is the estimated autocorrelation of the residuals at lag k.
The following hypotheses were adopted:
The p-values for each sector are significantly higher than the typical significance threshold (0.05), indicating that there is no evidence to reject the null hypothesis of no autocorrelation of the residuals. This provides further evidence that the models are a good fit to the data.
AIC and BIC are two statistics used to assess the quality of a statistical model and to compare different models, taking into account their fit to the data and the complexity of the model. Both AIC and BIC are frequently employed in time series analysis to identify the most suitable model. These values are calculated according to the following equation:
n is the number of observations;
k is the number of parameters in the model;
L is the maximum value of the plausibility function for the model.
In order to assess the suitability of the autoregressive models applied to the ODEX index data, both AIC and BIC were calculated in order to evaluate the quality of the models, as illustrated in
Table 5.
The AIC and BIC for industry are relatively low, indicating a good fit of the model given its complexity. However, the AIC and BIC for transport are higher than for industry, which may indicate that the model has greater complexity relative to the number of observations available, which may affect the overall quality of the fit. Furthermore, the AIC and BIC for households are higher, suggesting a potentially weaker model fit. In contrast, the AIC and BIC for overall are close to those for industry, indicating a relatively good model fit.
Over the last 15 years, EU legislation on energy efficiency has undergone significant changes. In 2023, the legislators increased the energy efficiency target, i.e., the target to reduce the EU’s final energy consumption, to 11.7% by 2030. A projection of the ODEX indicator for 2030 was therefore made. The results of the analyses carried out are presented in
Table 6.
The observed upward trend of the ODEX indicator in the short term, followed by a subsequent decline in the long term, may be indicative of a combination of time factors, technological progress and effective energy policies. Such results emphasise the importance of long-term planning and investment in energy efficiency, which are key to achieving sustainability and reducing environmental impacts.
In order to ensure the relevance and applicability of our projections for future energy efficiency trends in Poland, it is essential to consider them within a broader context. The projections made to 2030 are not only based on past and current data, but also take into account several key factors that could influence future outcomes. These include anticipated economic growth, expected advancements in energy-efficient technologies and potential changes in national and European energy policies.
For example, Poland’s economic growth, which directly impacts industrial activity and energy consumption, is projected by various economic forecasts to continue at a moderate pace. This growth will likely influence energy demand and efficiency trends in the industrial and household sectors. Furthermore, ongoing advancements in technology, such as the development and decreasing costs of renewable energy sources and energy-efficient appliances, are expected to play a critical role in shaping future energy consumption patterns.
Furthermore, policy decisions at both the national and European Union levels, such as commitments to reduce carbon emissions and improve energy efficiency, will significantly impact energy strategies within Poland. The European Green Deal and Poland’s Energy Policy 2040 are examples of such frameworks that aim to foster a significant shift towards more sustainable energy use over the next decade.
Including these contexts allows for a more comprehensive understanding of the projections, giving them weight and making them far from worthless. By acknowledging these factors, we provide a foundation for our projections that is both empirically grounded and informed by a comprehensive analysis of anticipated future developments.