Predicting the unemployment rate and energy poverty levels in selected European Union countries using an ARIMA-ARNN model

Data analysis

For this study we used the available data on Eurostat (2022b) extracting all the information for Sustainable Development Goal 7—Affordable and clean energy from the United Nations Department of Economic and Social Affairs (2022). In addition to an empirical data analysis, we also generated a graphical representation (Fig. 1) of the extracted values in order to better understand the trend energy poverty had over time in the considered countries and in comparison with the European average. As we can observe in the graphical image, the percentage of energy poverty population is below the European average in the developed countries (Hungary and Slovakia), while in the developing countries(Romania and Bulgaria) this percentage varies above the average value. It’s easy to see that for Bulgaria the energy poverty percentage is much higher than in EU27 and the other countries, even if in the recent years it had a continuous descending trend. For Hungary, Romania and Slovakia we notice that the percentage of population in energy poverty had a slightly ascending tendency in 2020 and 2021, most likely due to the COVID19 pandemic.

We estimate these percentages will continue to increase in the next period due to the actual political and economic situation in Europe.

Governments try to decrease the percentage of population that cannot afford to keep their home warm by introducing policies that facilitate renewable energy access and diminish the ascending trend of energy prices. Individuals and institutions started reducing their energy consumption in order to avoid the situation when they cannot afford the energy costs so as not to become energy poor (Residential Energy Efficiency (REE) Observatory in Central and Eastern Europe (CEE), 2022).

In our analysis we used the unemployment rate datasets for the last 23 years acquired from the World Bank (2022b). For a better visualisation of the data, we plotted the unemployment rate for the selected countries only for the last 17 years as shown in Fig. 2. We notice that the unemployment rate in the middle of 2022 in EU27 and in the considered countries as well, has nearly reached the same values as before the COVID19 pandemic presented by Ahmad et al. (2023) which produced a massive increase of unemployment in the summer of 2020 worldwide.

Further, for a better data analysis, we computed the Pearson correlation between the unemployment rate and the population unable to keep their home adequately warm by poverty status datasets, and for every country we compared each variable with the EU27 value. We can conclude that there is a positive correlation between these two variables. The results are summarized in Table 1 and all the values have correlations significant at the 0.01 level (two-tailed).

In the European Union the direction for the unemployment rate is given by the developing countries, their values having the most influence on the European unemployment average. The same goes for the percentages of the energy poverty population. The developed countries have values close to the European average in both cases, for unemployment rate and for energy poverty. The best correlation coefficient between the two variables is observed for Hungary dataset, mainly because the government policies manage to set a balance on the labor market, significantly reducing the untaxed work.

The unemployment rate serves as a key economic indicator, spanning various areas of interest, applied in investment policies because it is strongly correlated with the business rhythm and it’s dominant in monetary management. Forecasting the unemployment rate influences the decisions made in the socio-economic environment and we consider energy poverty as being one of the variables impacted by unemployment.

ARIMA-ARNN model

Over time, the AutoRegressive Integrated Moving Average (ARIMA) model has been extensively used for predicting stochastic time series with applications in economy, unemployment rate, inflation, stock market, electricity price, daily wind speed, traffic congestion, crime prediction, water treatment, energy consumption, air pollutants, daily solar energy production or COVID-19 pandemic (Parreno, 2022; Arun Kumar et al., 2022; Jinnah, Sahib & Ibrahim, 2022).

Analyzing different forecast examples in various fields, it can be observed that ARIMA obtains promising results and over time the predicted values proved to be comparable to the actual measured values. The ARIMA model relies on the linearity of time series and in many research studies the values are assumed to be linearly correlated which works fine for simple scenarios. However, the real world is more complex and there are many situations where time series also have a nonlinear component that needs to be addressed as well. In order to obtain satisfactory results, complex problems are more likely to be simulated using both the linear and nonlinear components of the time series values leading to a hybridisation of the considered model.

To capture the complex real world situations, a flexible tool has been used, namely artifical neural networks (ANN) described by Tealab (2018), which, in comparison with ARIMA, proved to be more effective only in some particular cases. An important feature of ANN models is their capability to design the time series nonlinear component by using multiple layers for interactions between the nonlinear neurons.

When modeling a time series with ARIMA, it was noticed that the model cannot seize the nonlinear side of these values; thus, it is necessary to use a different modeling technique that deals with the nonlinearity, such as the multilayer ANN model. Due to the heterogeneity of the time series components and their underlying patterns, a hybrid approach is suitable for obtaining accurate forecasting, reducing disparities of forecast errors of the involved models as proved by Buyuksahin & Ertekin (2019).

Since the ANN model is complex and it’s hard to find an optimal network architecture, a less complex and easier to describe model is recently preferred by researchers, being easily fitted to time series that uses its lagged values as inputs. This AutoRegressive Neural Network (ARNN) model described by Farhi & Yasir (2022) represents a feed-forward neural network with a single hidden layer.

Chakraborty et al. (2021) proposed an ARIMA-ARNN hybrid model and theoretically proved its asymptotic stationarity leading to accurate forecasting of wide time span series without increasing variance over time. They also show an example of applying the hybrid model on unemployment rate forecasting for several countries.

The residual errors generated by applying the ARIMA model on the time series after transforming it into a stationary one are then modeled using the nonlinear ARNN model.

ARIMA is a linear model with three parameters ARIMA(p, d, q), where p is the order of the autoregression model, q is the order of the moving average model and d is the level of differencing for converting the nonstationary time series into stationary. Based on the time series complexity, the differencing process may need to be repeated.

The ARIMA model is composed of two submodels, the AR model and the MA model, described mathematically as follows: (1)${\displaystyle Y{\left(AR\right)}_t=\alpha +{\beta }_{1}Y{\left(AR\right)}_{t-1}+{\beta }_{2}Y{\left(AR\right)}_{t-2}+\cdots +{\beta }_{p}Y{\left(AR\right)}_{t-p}}$

where Y(AR)_t are the lags of the series, β are the lags coefficients estimated by the model and α is the model’s intercept term. (2)${\displaystyle Y{\left(MA\right)}_t={ϵ}_t+{\theta }_1{ϵ}_{t-1}+{\theta }_2{ϵ}_{t-2}+\cdots +{\theta }_q{ϵ}_{t-q}}$

where Y(MA)_t depends only on the lagged forecast errors, θ are the parameters of the model and ϵ are unrelated error terms.

The mathematical expression of ARIMA model, as a combination of AR and MA models, is: (3)${\displaystyle Y_t=\alpha +\sum _{i=1}^p{\beta }_i{Y}_{t-i}+{ϵ}_t-\sum _{j=1}^q{\theta }_j{ϵ}_{t-j}}$

where Y_t and ϵ_t represent the time series and the random error at time t, β and θ are the coefficients of the model.

For estimating the p and q parameters of the AR and MA models we used plots for the autocorrelation function (ACF) and the partial autocorrelation function (PACF). Bayesian information criterion (BIC) and Akaike information criterion (AIC) presented by Vrieze (2012) were used to determine the best ARIMA model.

ARNN is a nonlinear modified neural network with two parameters ARNN(p, k), where p is the number of lagged inputs (from the AR part of the model) and k is the number of neurons from the hidden layer of the model. If the time series values are non-seasonal then the value of k is $\left[\frac{p+1}{2}\right]$. BIC is also used as the main test for choosing the best ARNN model. The mathematical expression of the ARNN model is: (4)${\displaystyle X_t={\varphi }_0\left\{w_{c_0}+\sum _k{w}_{k_0}{\varphi }_k\left(w_{c_k}+\sum _{i=1}^p{w}_{i_k}{X}_{t-j_i}\right)\right\}}$

where X_t is the time series at the moment t computed using the previous observations, w_c are the associated weights and ϕ represents the activation function.

The hybrid model considered for this study is ARIMA+ARNN (as shown in Fig. 3): (5)${\displaystyle Z_t=Y_t+X_t}$

where Y_t is the linear component obtained using the ARIMA model and X_t is the nonlinear component computed with the ARNN model.

The residuals autocorrelations that could not be modeled by ARIMA are introduced in ARNN that models them leading to improvement of the original forecasts. The method used for forecasting using this hybrid model can be summarized in the following steps:

1. Determine the most appropriate parameters p, d, q for ARIMA, using the ACF and PACF plots and AIC and BIC coefficients;

2. Apply previously determined ARIMA(p,d,q) model for the training data set;

3. Determine the forecast values and residual errors from the ARIMA implementation;

4. Import residuals in the ARNN(p,k) model;

5. Compute the forecast values of the ARNN model;

6. Obtain the final forecast by combining the forecasts of ARIMA and ARNN.

Results

The ARIMA-ARNN hybrid model is used in our study for predicting the unemployment rate and energy poverty percentage thus analyzing the connection between the two variables.

Time series associated with the unemployment rate of a country is nonlinear and nonstationary; therefore, a hybrid prediction model would be the most appropriate for dealing with these variations in the data. The hybrid model has been theoretically demonstrated and it seems to be asymptotic stationary when forecasting over large periods of time.

We tested the stationarity of every dataset using the augmented Dickey-Fuller (ADF) test (Dickey & Fuller, 1979; Cheung & Lai, 1995). Almost all of the series were nonstationary when first applying the ADF test, but, after applying first order differencing, all the series failed to reject the null hypothesis of stationarity, thus giving the value 1 for the differencing parameter of the ARIMA models.

The unemployment rate datasets, distributed over almost 23 years, between 2000 and 2022, are divided into training sets and test sets (12 months).

First, we applied the model on the unemployment rate for the considered datasets and obtained the following results:

• For EU27, ARIMA(5, 1, 5) was the best obtained option, having AIC −167.075. We extracted the residuals from ARIMA and trained them further, obtaining the ARNN(24,12) model. Then we extracted the predictions from the ARIMA+ARNN model, comparing them with the test dataset and obtaining the following accuracy: RMSE = 0.144, MAE = 0.128.

• For Bulgaria, ARIMA(5,1,4) was the best option, having AIC 53.277. The residuals extracted from ARIMA were trained further, obtaining the ARNN(12,6) model. The ARIMA+ARNN model was applied, predictions were computed and then they were compared with the test dataset: RMSE =0.118, MAE =0.094.

• For Hungary, we obtained AIC 230.241 for ARIMA(5,1,5) and ARNN(15,8) with an average of 20 networks. Forecasts were extracted from the ARIMA+ARNN model, obtaining an accuracy of RMSE = 0.310, MAE = 0,275.

• For the Romanian dataset we obtained ARIMA(4,1,3) with an AIC = 228.33. Its residuals were trained with the ARNN(12,6) model and then we applied the hybrid ARIMA+ARNN model, with the following accuracy: RMSE = 0.257, MAE = 0.214.

• For Slovakia, the best ARIMA was for p = 2, d = 1, q = 3 with AIC = 40.112 and the best ARNN model for residuals training was ARNN(24,12). Then, the accuracy of RMSE = 0.082 and MAE = 0.074 were obtained by computing the predictions with the ARIMA+ARNN model.

For every residual series collected from the ARIMA models we used the Ljung–Box portmanteau test (Ljung, 1986) with five lags, in order to examine if the residuals are independently distributed. The p-values we obtained are greater than 0.05, therefore confirming the null hypothesis: EU27 p-value = 0.890, Bulgaria p-value = 0.409, Hungary p-value = 0.942, Romania p-value = 0.876, Slovakia p-value = 0.758.

Based on the results described above and considering the accuracy of the hybrid model we can use the model to obtain forecasts for the following 12 months. In Fig. 4, for every country and also for EU27, we represented with blue 24 months of actual unemployment rate values, the next 12 months are illustrated with blue for the actual values (test dataset) and with red for the predicted values obtained from the hybrid model, while the forecast values for unemployment rate are displayed in red for the final 12 months in the graphical representation.

The energy poverty datasets were split into training sets (2005–2020) and testing sets for 2021 (12 months).

Secondly, we applied the model on the energy poverty percentages for the collected datasets and obtained the following results:

• For EU27, ARIMA(4, 1, 4) was the best option having AIC 277.494. We extracted the residuals from ARIMA and trained them further, obtaining the ARNN(12,6) model with an average of 20 networks. Then, we extracted the predictions from the ARIMA+ARNN model, comparing them with the test dataset and obtaining the following accuracy: RMSE = 0.267, MAE = 0.194.

• For Bulgaria, an AIC of 694.454 was obtained for ARIMA(2, 1, 1) and, further, ARNN(5,3) was applied on the ARIMA residuals. An accuracy of RMSE = 0.216, MAE = 0.316 was retrieved for the hybrid ARIMA+ARNN model’s predictions.

• For Hungary, ARIMA(3, 1, 2) was fitted on the training dataset with an AIC = 264.814. The derived residuals were then processed with the ARNN(12,6) model with an average of 20 networks, each of which is a 12-6-1 network with 85 weights. The final predictions from the hybrid ARIMA+ARNN model were compared with the test dataset obtaining: RMSE = 0.299, MAE = 0.254.

• For Romania, we obtained ARIMA(1,1,2) having AIC = 401.665 and ARNN(3,2) models. The predictions derived from both ARIMA and ARNN models are combined in order to determine the final test forecasts that led to the following accuracy values: RMSE = 0.216, MAE = 0.171.

• For Slovakia, forecasts were extracted from the hybrid ARIMA+ARNN model, based on ARIMA(1,1,1) with AIC 290.410 and ARNN(1,1) models, for which RMSE = 0.171 and MAE = 0.162 were computed.

The Ljung–Box test was again applied for the residual data obtained from ARIMA models, demonstrating the model performance: EU27 p-value = 0.642, Bulgaria p-value = 0.999, Hungary p-value = 0.907, Romania p-value = 0.706, Slovakia p-value = 0.892.

In Fig. 5, we plotted with blue lines the actual values of percentage of population in energy poverty for the last 24 months of the training dataset plus 12 months of the testing set compared to the testing prediction, followed by future 12 months forecasts. All the predictions were represented in our graphical interpretation using red lines.

Discussion

Analyzing the forecasts we obtained from the hybrid model, we observe that, for unemployment, Bulgaria and Hungary are below the EU average, Romania is slightly below the average, while Slovakia has a similar trend compared to the European average.

Energy poverty forecasts present obvious differences between the developed and the developing countries. The two developed countries, Slovakia and Hungary, have lower energy poverty percentages than in EU27, while the developing countries, Romania and Bulgaria, have much higher percentages of energy poverty.

Bulgaria has a low unemployment rate, but has the highest energy poverty percentage among the four analyzed countries, because they have a low income, their houses have poor energetic efficiency although energy prices are lower than other countries in EU. The Bulgarian policies concerning energy poverty were applied mostly on dwellings rehabilitation and financial aid for the vulnerable population.

Romania is above the European average both on the income percentage spent on energy bills and also on the percentage of households that self-impose restrictions in order to decrease their energy expenditure. Energy prices in this country are slightly below the European mean, but the average income is much lower compared to the developed countries. Governmental policies are mainly focused on providing financial aid for households with low income. These regulations are disadvantageous for hidden energy poverty individuals, pushing them to restrict their consumption thus reducing their living confort. Houses rehabilitation and renovation policies are developed for the general population and do not apply specifically to energy poverty.

Compared to the developing countries, the developed ones tend to have a lower level of energy poverty. One of the main reasons is that they have a higher average income and so the hidden poverty has a reduced rate.

In Hungary, both energy poverty percentage and unemployment rate are below the European average, as well as the households energy costs. Governmental policies created procedures for protecting different categories of vulnerable consumers. In order to inhibit the increased price issues, the government took measures to cap the prices for all population. Policies were also provided for all household renovations. All of these measures led to keeping the energy poverty percentage at a low level.

In Slovakia, we notice that the unemployment rate forecasts are similar to the European average, while the energy poverty percentage is much lower than the same median, mainly due to the fact that household energy costs were somewhat constant over time. The main policies regarding energy poverty involve financial assistance for low income individuals. The general population doesn’t benefit from many facilities that allow it to improve household energy efficiency.

Analyzing the collected data for the selected countries, we observed that unemployment rate and energy poverty percentage are interconnected, having comparable tendencies. Using the hybrid model we obtained predictions for unemployment and energy poverty. We conclude that both forecasts are still connected, having similar directions. Unemployment and energy poverty will continue to be strongly correlated, unless governments take measures to diminish the impact that the other aspects have on energy poverty.