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Part 1. From Transition Growth to a New High

Croatia’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 gives a compact summary of long-run growth, recession, recovery and cyclical instability. In this blog post, Croatia’s GDP is analysed as a quarterly index, with 2021=100, covering the period from 1995Q1 to 2026Q1. The data source is Eurostat’s quarterly national accounts dataset, namq_10_gdp. Two versions of the series are considered: the original series and the seasonally adjusted series obtained using X13-ARIMA.

Figure 1 shows three large macroeconomic phases. The first is the long expansion from the mid-1990s to 2008. GDP rises steadily, with the seasonally adjusted series showing a clear upward trend and the original series showing strong quarterly seasonal movement around that trend. The second phase begins with the global financial crisis. Around 2008–2009, the previous expansion breaks, and the series enters a long period of weakness. Unlike some economies where the post-crisis recovery was rapid, Croatia’s GDP remains subdued for several years. The graph shows a prolonged period of stagnation and only gradual recovery through the first half of the 2010s. The third phase begins from the mid-2010s, when the series resumes a clearer upward path. This expansion is interrupted sharply by the COVID-19 shock in 2020, followed by a very strong rebound and a new high in the latest part of the sample.

The pandemic episode is especially visible. Croatia’s GDP falls sharply in 2020 and then rebounds strongly. The magnitude of the swing is larger than in many other former Yugoslav economies, which is consistent with the importance of tourism and services in Croatia’s economy. The latest observations remain high by historical standards, but the cyclical indicators discussed later suggest that the economy is no longer in the same rapid rebound phase. The level of GDP is high, but the position around trend has become more moderate.

Seasonal adjustment is essential for this series. The original GDP index shows a strong within-year pattern, with clear quarterly peaks and troughs. Without seasonal adjustment, one might confuse regular seasonal movement with a genuine change in economic momentum. The seasonally adjusted series therefore provides a cleaner view of trend and cycle, while the original series remains useful because it reminds us how strong the raw seasonal pattern is.

Figures 2 and 3 show the persistence of the Croatian GDP series before and after differencing. The autocorrelation function of the log-level series is strongly positive over many lags. The first autocorrelation is about 0.797, and the cumulative autocorrelation measure is also high. This means that the level of GDP in one quarter is strongly related to the level in previous quarters. This is expected for a macroeconomic level variable: GDP reflects accumulated productive capacity, investment, employment, external demand, institutions and policy settings, none of which changes randomly from quarter to quarter.

Figure 3 changes the picture. After first differencing and seasonal differencing of the log series, autocorrelations become much weaker, and the first autocorrelation is close to zero, around -0.012. This means that differencing has removed much of the persistent trend and seasonal structure. The differenced series is therefore more suitable for ARIMA modelling, where the objective is not to describe the long-run level but to model short-run movements after the dominant trend and seasonality have been accounted for.

Table 1 confirms that Croatia’s GDP is a highly structured time series. Trend strength is very high, around 0.995, which indicates that the long-run component dominates the series. Seasonal strength is also very high, around 0.977. The seasonal peak is in the third quarter, while the seasonal trough is in the first quarter. This is economically intuitive for Croatia, given the strong summer-season profile of parts of the economy. The spikiness value is very low, meaning that the series is not dominated by random isolated spikes, even though the pandemic creates one very large visible disturbance.

Table 1. Features of GDP for Croatia time series

Feature	Value
trend_strength	0.995
seasonal_strength_year	0.977
seasonal_peak_year	3
seasonal_trough_year	1
spikiness	0.000
linearity	1.944
curvature	-0.179
stl_e_acf1	-0.182
stl_e_acf10	0.275
acf1	0.797
acf10	4.259
diff1_acf1	-0.012
diff1_acf10	4.064
diff2_acf1	-0.054
diff2_acf10	3.881
season_acf1	0.860
pacf5	1.513
diff1_pacf5	1.424
diff2_pacf5	1.539
season_pacf	0.161
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	2.163
kpss_pvalue	0.010
pp_stat	-3.302
pp_pvalue	0.022
ndiffs	1
nsdiffs	1
bp_stat	79.446
bp_pvalue	0.000
lb_stat	81.368
lb_pvalue	0.000
var_tiled_var	0.007
var_tiled_mean	0.841
shift_level_max	0.126
shift_level_index	106
shift_var_max	0.017
shift_var_index	103.000
shift_kl_max	0.425
shift_kl_index	105
spectral_entropy	0.323
n_crossing_points	33
longest_flat_spot	2
coef_hurst	0.996
stat_arch_lm	0.934

The linearity measure is positive and relatively large, while curvature is negative. This combination suggests a broadly rising long-run path, but not one that grows at a constant rate. The STL residual autocorrelation at the first lag is negative, while the longer-lag residual autocorrelation remains positive, indicating that some structure remains even after decomposition. The ACF and PACF features show strong persistence in levels, weaker dependence after differencing and meaningful seasonal dependence. The seasonal autocorrelation is about 0.860, reinforcing the importance of quarterly seasonality.

The stationarity diagnostics point strongly toward non-stationarity in the level series. The KPSS statistic is high, with a p-value at the lower bound, while the Phillips-Perron statistic is also significant. The automatic differencing indicators recommend one ordinary difference and one seasonal difference. The Box-Pierce and Ljung-Box statistics are highly significant in levels, which is consistent with the visible persistence in the autocorrelation function. The zero-run and zero-proportion indicators are zero, as expected for a continuous GDP index rather than a count series with repeated zeros. The Guerrero lambda is negative, supporting the use of transformation. The variance-tile and shift indicators show changes in level and variability, with important shifts around the post-pandemic part of the sample. Spectral entropy is moderate-low, around 0.323, which means the series is structured rather than noisy. The number of crossing points is limited, the longest flat spot is short, and the Hurst coefficient is close to one, confirming long memory. The ARCH statistic is not large enough to make volatility clustering the central feature of the series; the dominant features are trend, seasonality and persistence.

The main conclusion from Part 1 is that Croatia’s quarterly GDP is a strongly trending, highly seasonal and persistent macroeconomic series. Its path is shaped by a long pre-2008 expansion, a prolonged post-crisis weakness, renewed growth, a deep pandemic shock and a strong recovery. These properties justify the use of log transformation, seasonal adjustment, differencing and ARIMA modelling in the next part.

Methodological appendix to Part 1

Graphical exploration is the starting point of time-series analysis. It helps identify trends, cycles, seasonal patterns, structural breaks, changes in volatility and outliers. In quarterly GDP data, the main pitfall is confusing regular seasonal movement with genuine macroeconomic change. Another risk is over-interpreting one unusual observation without checking whether it is part of a broader pattern.

The log transformation is used because macroeconomic series often become more variable in absolute terms as their level 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 indicators and Hurst persistence jointly show whether a series is trending, seasonal, persistent, noisy or structurally unstable. For Croatia, they confirm a highly structured, non-stationary GDP series.