Part 1. From steady convergence to a mature high-income cycle
Slovenia’s GDP as a quarterly time series
Gross domestic product is the broadest single indicator of macroeconomic activity. It measures the value of goods and services produced in an economy and therefore provides a compact summary of long-run expansion, recession, recovery and cyclical instability. In this blog post, Slovenia’s GDP is analysed as a quarterly index, with 2021=100, covering the period from 1996Q1 to 2026Q1. The data source is Eurostat’s quarterly national accounts dataset, namq_10_gdp. Two versions of the series are examined: the original series and the seasonally adjusted series obtained using X13-ARIMA.
Figure 1 shows a long upward movement in Slovenia’s GDP, interrupted by two large macroeconomic shocks. The first part of the sample, from the late 1990s to 2008, is a sustained expansion. The seasonally adjusted line rises almost continuously, suggesting a long period of convergence and growth. The global financial crisis then marks a clear break. Around 2008–2009, the previous upward path is interrupted, and the series enters a prolonged period of weaker performance. The post-crisis years do not show an immediate return to the pre-crisis path. Instead, there is a long adjustment phase, with GDP moving sideways or only gradually upward.
From the mid-2010s, the series resumes a more convincing upward trajectory. This expansion continues until the COVID-19 shock in 2020. The pandemic decline is sharp and visible, but the rebound is also strong. By the later part of the sample, Slovenia’s GDP is again on a high historical level. The most recent observations remain close to the upper end of the sample range, although the movement looks more like a mature expansion with some moderation than a new acceleration.
Seasonal adjustment is important but not the whole story. The original series has a clear quarterly pattern, while the X13-adjusted series gives a cleaner view of the underlying trend and cycle. In Slovenia’s case, the seasonal pattern is visible but less dominant than in economies with very strong tourism-related quarterly swings. The main time-series story is therefore the combination of long-run trend, strong persistence and two major interruptions: the global financial crisis and COVID-19.
Figures 2 and 3 show how persistent Slovenia’s GDP is before and after differencing. The autocorrelation function of the log-level series is very high and remains positive across many lags. The first autocorrelation is about 0.940, indicating that GDP in one quarter is very closely related to GDP in the previous quarter. This is typical of a macroeconomic level series. GDP reflects accumulated productive capacity, employment, investment, productivity, external demand and institutions, all of which evolve gradually.
Figure 3 changes the picture sharply. After applying first and seasonal differences to the log series, autocorrelation becomes much weaker and turns negative at the first lag, around -0.522. The second-difference autocorrelation is even more negative, around -0.726. This suggests that differencing removes the dominant persistent trend and seasonal structure and reveals shorter-run adjustment dynamics. In practical terms, the log-level series is useful for understanding Slovenia’s long-run macroeconomic path, while the differenced series is more suitable for ARIMA modelling and short-term forecasting.
Table 1 confirms that Slovenia’s GDP is a highly structured time series. Trend strength is extremely high, around 0.998, which means that the long-run component dominates the series. Seasonal strength is also high, around 0.890, confirming that seasonal adjustment is necessary. The seasonal indicators show a regular within-year pattern, though the seasonal amplitude is less visually overwhelming than in Montenegro or Croatia. The spikiness value is extremely low, meaning that the series is not driven by isolated random spikes. Even the global financial crisis and COVID-19 occur within a broader structured trajectory rather than as purely erratic movements.
Table 1. Features of GDP for Slovenia time series
| Feature | Value |
|---|---|
| trend_strength | 0.998 |
| seasonal_strength_year | 0.890 |
| seasonal_peak_year | 0 |
| seasonal_trough_year | 1 |
| spikiness | 0.000 |
| linearity | 2.126 |
| curvature | -0.223 |
| stl_e_acf1 | -0.413 |
| stl_e_acf10 | 0.223 |
| acf1 | 0.940 |
| acf10 | 6.517 |
| diff1_acf1 | -0.522 |
| diff1_acf10 | 2.366 |
| diff2_acf1 | -0.726 |
| diff2_acf10 | 3.678 |
| season_acf1 | 0.867 |
| pacf5 | 1.121 |
| diff1_pacf5 | 0.994 |
| diff2_pacf5 | 1.211 |
| season_pacf | 0.238 |
| zero_run_mean | 0.000 |
| nonzero_squared_cv | 0.002 |
| zero_start_prop | 0.000 |
| zero_end_prop | 0.000 |
| lambda_guerrero | -0.900 |
| kpss_stat | 2.294 |
| kpss_pvalue | 0.010 |
| pp_stat | -2.016 |
| pp_pvalue | 0.1 |
| ndiffs | 1 |
| nsdiffs | 1 |
| bp_stat | 106.906 |
| bp_pvalue | 0.000 |
| lb_stat | 109.579 |
| lb_pvalue | 0.000 |
| var_tiled_var | 0.000 |
| var_tiled_mean | 1.016 |
| shift_level_max | 0.088 |
| shift_level_index | 102 |
| shift_var_max | 0.004 |
| shift_var_index | 50 |
| shift_kl_max | 0.287 |
| shift_kl_index | 51 |
| spectral_entropy | 0.212 |
| n_crossing_points | 13 |
| longest_flat_spot | 6 |
| coef_hurst | 1.000 |
| stat_arch_lm | 0.954 |
The linearity measure is positive and relatively large, while curvature is negative. This suggests a long-term upward path, but one that changes slope across the sample. The STL residual autocorrelation is negative at the first lag but positive over longer lags, meaning that some structure remains even after decomposition. The ACF and PACF measures show strong persistence in levels, weaker but meaningful dependence after differencing and a visible seasonal component. The seasonal autocorrelation is about 0.867.
The stationarity diagnostics strongly suggest that the level series should not be treated as stationary. The KPSS statistic is high, with a p-value at the lower bound, and the automatic differencing indicators recommend one ordinary difference and one seasonal difference. The Phillips-Perron result is less restrictive, but it does not overturn the broader conclusion that the level series behaves like a persistent macroeconomic time series. The Box-Pierce and Ljung-Box statistics are highly significant in levels, confirming strong serial dependence. The variance and shift indicators point to changes in level and distribution, especially around the later part of the sample. Spectral entropy is low, around 0.212, indicating that the series is structured rather than noisy. The Hurst coefficient is almost one, confirming strong long-memory behaviour. The ARCH statistic is modest, so volatility clustering is not the central feature of the series.
The main conclusion from Part 1 is that Slovenia’s quarterly GDP is a strongly trending, highly persistent and seasonally structured series. Its long-run path is upward, but it is interrupted by a deep global-financial-crisis adjustment and by the shorter COVID-19 shock. These properties justify the use of log transformation, seasonal adjustment, differencing and ARIMA modelling.
Methodological appendix to Part 1
Graphical exploration is the first step in time-series analysis. It helps identify trend, seasonality, cyclical movement, structural breaks, volatility changes and outliers. In quarterly GDP data, the main risk is confusing normal seasonal movement with genuine macroeconomic change. Another risk is over-interpreting one unusual observation without checking whether it belongs to a broader pattern.
A log transformation is often useful when macroeconomic fluctuations become larger in absolute terms as the level of the series rises. Logs make movements easier to interpret as approximate percentage changes. First differences focus on short-run change, while seasonal differences compare a quarter with the same quarter in the previous year and help remove recurring seasonal patterns. The features in Table 1 summarise the statistical behaviour of the series. Trend strength, seasonal strength, autocorrelation, stationarity tests, entropy, spikiness, shift measures and persistence indicators jointly show whether a series is trending, seasonal, persistent, noisy or structurally unstable. For Slovenia, the dominant message is very strong trend persistence, meaningful seasonality and a highly structured macroeconomic path.