**4. Methodology**

The data used for our empirical models was accessed in December 2019 via Eurostat, a European Statistical Office. Some of the latest data are for 2018 (GDP), but others are for 2017 (e.g., GHG), which is given by the data availability and accessibility.

For forecasting time series, a popular and widely used statistical method called ARIMA [67–69] has been used. ARIMA is an acronym for Auto Regressive Integrated Moving Average. AR is a class of linear model where the variable of interest is regressed on its own lagged values. MA is also class of linear model, where the variable of interest is modeled with its own imperfectly predicted values of current and previous times [70]. The I is an integration—it specifies the number of times the differencing operation is performed on a series to make it stationary.

The Auto Regression (AR) process is written as

$$\mathbf{y\_t = \phi\_1 y\_{t-1} + \phi\_2 y\_{t-2} + \dots + \phi\_p y\_{t-p} + \varepsilon\_t}$$

where:

> φ<sup>t</sup>−1—parameters; yt−i—regressors; —error. Moving Average (MA) can be written in terms of error terms:

$$\mathbf{y}\_{\mathsf{t}} = \boldsymbol{\Theta}\_{1}\boldsymbol{\epsilon}\_{\mathsf{t}-1} + \boldsymbol{\Theta}\_{2}\boldsymbol{\epsilon}\_{\mathsf{t}-2} + \cdots + \boldsymbol{\Theta}\_{\mathsf{d}}\boldsymbol{\epsilon}\_{\mathsf{t}-\mathsf{d}} + \boldsymbol{\epsilon}\_{\mathsf{t}}$$

where:

> θ<sup>t</sup>−1—parameters;

t−i—regressors—imperfections (errors) in predicting previous terms; —error.

The ARMA process has the mathematical form:

$$y\_t = \sum\_{i=1}^p \Phi\_i y\_{t-i} + \sum\_{j=1}^q \Theta\_i \mathbf{e}\_{t-j} + \mathbf{e}\_t$$

As a result, the differencing is the ARIMA process. The "predictors" on the right-hand side include both the lagged values of yt and the lagged errors. We call this an ARIMA (p, d, q) model, where parameters (p, d, q) describe:

AR: p—periods to lag;

I: d—the degree of differencing;

MA: q—the lag of the error component.

All figures used hereinafter in this paper and employed for comparing the situation in Czech Republic and Slovakia were prepared separately for Czech Republic and Slovakia due to one simple fact that the scale of data was different and it would not look clear and comparable if placed on the same figure.

Moreover, we should also explain that the confidence interval (Lo-Hi) of a forecast (shadow on figures) is the range within which the value we forecast will lie with a certain probability. For example, if, for GHG for Slovakia in 2018, the Lo.95-Hi.95 percent of the forecast confidence interval is between 40.09 and 48.38, then with a probability of 95%, GHG (greenhouse gas emission) will be at least 40.09 Mt and at most 48.38 Mt.

The empirical models used hereinafter is based on our previous similar studies covering other EU countries (e.g., Poland) and focusing on the same issues (see, e.g., [71]).

## **5. Results and Discussions**

Our results are outlined below as follows: First, let us look at the greenhouse gas emission (GHG) in the Czech Republic. The dashed line in Figure 1 represents the GHG emission limit for 2020. For the Czech Republic it is no more than 9% comparing to year 2005 (149.53 Mt). It means that the limit for 2020 equals 162.99 Mt. The emissions are decreasing (even taking into the account the high and low forecast as shown in Figure 1).

**Figure 1.** GHG emissions in Czech Republic in 1990–2020 (Source: Own results).

Table 2 depicts the values presented in Figure 1 in more detail, including the forecast, as well as forecast for the values of Hi and Lo at 80% and 95%, respectively, for the Czech Republic.

**Table 2.** Forecast Auto Regressive Integrated Moving Average (ARIMA) (0,1,0) details for GHG emissions in Czech Republic (Source: Own results).


Our key conclusion stemming from the analysis of GHG emissions in Czech Republic is that the country is likely to meet the requirements of Europe 2020 in terms of greenhouse gas emissions (GHG), because from 2007 onwards the trend is towards a continuous reduction in greenhouse gas emissions.

Looking into the case of Slovakia, one can see the following story (see Figure 2 that follows). For Slovakia the GHG limit is no more than 13% comparing to year 2005 (51.28 Mt). It means the limit for 2020 equals 57.95 Mt.

Table 3 depicts the values presented in Figure 1 in more detail, including the forecast, and the Hi and Lo at 80% and 95%, respectively, for Slovakia.

**Table 3.** Forecast ARIMA (2,1,0) details for GHG emissions in Slovakia (Source: Own results).


**Figure 2.** GHG emissions in Slovakia in 1990–2020 (Source: Own results).

The key conclusions for Slovakia that were obtained appear to be similar to in the situation in the Czech Republic. Figure 3 shows the share of renewable energy sources (RES) in the Czech Republic.

**Figure 3.** Share of renewable energy sources in gross final energy consumption in the Czech Republic (Source: Own results).

The share of renewable energy in Czech Republic has been growing and since 2005 has always been under Europe 2020 target (see Table 4).


**Table 4.** Forecast ARIMA (0,1,0) details for the share of renewable energy sources in the Czech Republic (Source: Own results).

Even the most pessimistic forecasts (Lo.95) show that the RES will be above the assumed level of 13%. Figure 4 above show the results of the similar simulation for Slovakia.

**Figure 4.** Share of renewable energy sources in gross final energy consumption in Slovakia (Source: Own results).

From Figure 4 and Table 5 one can deduct that the maximum share of renewable energy in Slovakia was in 2015, and since this year has been decreasing. Therefore, it is improbable that Slovakia will achieve Europe 2020 goals in the RES indicator.

**Table 5.** Forecast ARIMA (0,1,0) details for the share of renewable energy sources in Slovakia (Source: Own results).


Figure 5 and Table 6 shows the primary energy consumption and final energy consumption (PEC, FEC) for the Czech Republic.

**Figure 5.** Primary energy consumption in the Czech Republic (Source: Own results).

**Table 6.** Forecast ARIMA (1,0,0) details for the primary energy consumption in the Czech Republic (Source: Own results).


Overall, it seems that for the Czech Republic primary and final energy consumption have both been fluctuating around their Europe 2020 target (see Figure 6 and Table 7). Based on the forecast, we can assess that the target will be slightly exceeded, but the confidence interval of the forecast gives hope that it could be under the limit. Figure 7 and Table 8 shows the results from a similar simulation for the case of Slovakia.

**Figure 6.** Final energy consumption in the Czech Republic (Source: Own results).


**Table 7.** Forecast ARIMA (0,2,1) details for the primary energy consumption in the Czech Republic (Source: Own results).

**Figure 7.** Primary energy consumption in Slovakia (Source: Own results).

**Table 8.** Forecast ARIMA (0,1,0) details for the primary energy consumption in Slovakia (Source: Own results).


The main conclusions here is that the primary energy consumption in Slovakia has been under the Europe 2020 limit since 2011, but since 2014 we can observe change in the trend—PEC growth. It appears quite difficult to assess what the result in 2020 will be, but our simulations and forecast show it will be very close to the limit.

Final energy consumption for Slovakia was set on an unattainable level for this country. Slovakia has never been close to this level and seems improbable to achieve this level in 2020 (see Figure 8 and Table 9).

**Table 9.** Forecast ARIMA (0,1,0) details for the final energy consumption in Slovakia (Source: Own results).


**Figure 8.** Final energy consumption in Slovakia (Source: Own results).

**Figure 9.** Gross domestic product in current and constant prices in the Czech Republic (Source: Own results).

In general, there is no forecast of GDP, because it does not constitute any importance for Europe's 2020 strategy and its implications. Nevertheless, is seems important to describe how it looked like in the past, because GDP is used for energy intensity calculation and forecast (see the next figures that follow) and is also important for sustainable development. Figure 10 below shows the gross domestic product in current prices in Slovakia.

**Figure 10.** Gross domestic product in current and constant prices in Slovakia (Source: Own results).

The results for Slovakia seem to be very much the same as for Czech Republic. Furthermore, let us look at Figure 11 that shows real GDP growth rate in EU compared to the Czech Republic and Slovakia.

**Figure 11.** Real GDP growth rate in the EU compared to the Czech Republic and Slovakia (Source: Own results).

The differences between the Czech Republic and Slovakia are quite obvious. Slovakia is growing at a faster pace. This might be attributed to the better and more efficient economic reforms in Slovakia

that accepted the Euro as its currency in 2009 while the Czech Republic still keeps its national currency, the Czech koruna.

Figures 12 and 13 that follow shows the energy intensity in the Czech Republic and Slovakia that is calculated as the ratio of gross inland energy consumption (GIEC) to GDP. The two different shapes of energy intensity depict the (i) forecast, (ii) forecast Lo 80% and 95%, as well as (iii) forecast Hi 80% and 95% for each country, respectively (see Tables 10 and 11 for more explanation showing the values for each forecast).

**Figure 12.** Energy intensity in the Czech Republic expressed as GIEG/GDP with forecast, forecast Lo 80% and 95% and forecast Hi 80% a and 95% (Source: Own results).

**Figure 13.** Energy intensity in Slovakia expressed as GIEG/GDP with forecast, forecast Lo 80% and 95% and forecast Hi 80% a and 95% (Source: Own results).



**Table 11.** Forecast ARIMA (0,1,0) details for the energy intensity in Slovakia GIEG/GDP with forecast, forecast Lo 95% and forecast Hi 95% (Source: Own results).


The low value of energy intensity speaks of the level of economic development. The average for the EU equals 0.1097. The energy intensity of Czech Republic is twice larger than the average for the EU but it has a decreasing trend. Figure 13 below shows the same situation but using the case of Slovakia. It is apparent that the Slovak energy intensity also exceeds the EU average.

The main conclusions stemming from Figures 12 and 13 and the accompanying tables are that the low value of energy intensity speaks of the modern economy. The EU average equals 0.1097. Energy intensity of Slovakia is twice larger than the average of the EU and decreased fast between 1995 and 2007, but in the last years the decrease is very slow and looks to be stabilizing.

Figure 14 depicts energy consumption and greenhouse gas emissions for the Czech Republic.

**Figure 14.** Gross inland energy consumption (GIEC) and GHG emissions in the Czech Republic (Source: Own results).

In the case of the Czech Republic, GIEC and GHG are correlated, but we can see that in the last years GHG emission is decreasing faster than the energy consumption. This is, of course, a positive trend that can be attributed to the improvement in energy policy and strategy.

All in all, also in the case of Slovakia, the GIEC and GHG appear to be correlated. It is apparent from Figure 15 that in the last years, GHG emission is decreasing a little faster than energy consumption, but not as fast as in the case of the Czech Republic that was analyzed above. This was shown on the previous figures describing the renewable energy sharing system.

**Figure 15.** Gross inland energy consumption (GIEC) and GHG emissions in Slovakia (Source: Own results).
