A seasonal view of a small open economy

1. Introduction

Real gross domestic product is the basic yardstick economists use to track how an economy evolves through time. For Bosnia and Herzegovina, real GDP in chain-linked volumes with 2020 as the base year summarises a quarter of a century of post-war reconstruction, transition, integration with European markets and exposure to global shocks. The quarterly series from 2000 to mid-2025 condenses this history into a single curve, but to interpret it sensibly we need to peel away the regular seasonal swings and the short-lived noise that obscure the underlying path.

The graphs considered here show real GDP for Bosnia and Herzegovina in logarithms, along with seasonal adjustment and decompositions based on STL, a widely used procedure that splits a time series into trend, seasonal and irregular components using locally weighted regressions. By working mostly with the log series, and then with first and seasonal differences of that log series, the analysis emphasises proportional changes rather than absolute levels and makes it easier to study growth rates and volatility.

The period from 2000 to around the eve of the global financial crisis is one of catch-up growth as the country rebuilds its productive capacity and institutions. Real GDP rises steadily, albeit with noticeable seasonal ups and downs associated with construction, trade and tourism. The GFC marks the first major interruption to this pattern, with a slowdown and a temporary dip in output that mirrors the broader European downturn. The 2010s bring renewed but more moderate growth, followed by a brutal but short-lived collapse in 2020 when the COVID-19 pandemic freezes mobility and demand. In the most recent years, the series points to a recovery, although growth appears to have normalised at rates closer to those in neighbouring European economies than to the high catch-up rates of the early 2000s.

Seen in this light, Bosnia and Herzegovina’s real GDP series is both a local story and a regional one. It reflects domestic structural reforms, investment and political uncertainty, but it also echoes EU-wide cycles, shifts in global risk appetite and shocks to international trade and tourism. The rest of the post walks through the evidence contained in the ten graphs, starting from the log-level series and drilling down into seasonal diagnostics and growth rates.

2. Description of the time series and components

2.1 Log levels and seasonally adjusted series

The first graph in Figure 1 shows the log of real GDP together with its STL-based seasonally adjusted counterpart. Working in logs has two advantages: it compresses the vertical scale, making early and late observations more comparable, and it makes equal vertical distances correspond roughly to equal percentage changes.

From 2000 to 2008 the log series slopes upward at a fairly steady pace, indicating rapid real growth in the pre-crisis expansion. Seasonal fluctuations are visible as regular oscillations around this rising path, but the underlying trend is clearly positive. The seasonally adjusted line smooths away most of this intra-year zigzag, revealing an almost monotonic rise.

Around 2008–2009 the slope of the adjusted series flattens and briefly turns down, marking the impact of the global financial crisis. Bosnia and Herzegovina, like many small open economies in the region, experienced a contraction as demand from the European Union fell and financing conditions tightened. The downturn is not as extreme as what will later occur during COVID-19, but it is the first visible break in the trend.

In the early 2010s the adjusted series recovers its upward trajectory, although the slope now appears somewhat gentler, consistent with medium-term growth in the low- to mid-single digits rather than the very high rates seen immediately after 2000. Seasonal swings continue, but their amplitude in logs looks broadly stable, suggesting that proportional seasonal effects have not grown over time.

The most dramatic movement comes in 2020. Both the original and seasonally adjusted log series plunge, indicating a sharp contraction in real GDP when lockdowns, travel restrictions and global uncertainty hit the economy. The drop is followed by a strong rebound, with the adjusted series quickly clawing back much of the lost ground. In the last few years leading up to 2025Q1, the adjusted path resumes a gentle upward slope. The level of real GDP is higher than before the pandemic, but the series does not show an explosive boom; instead, it suggests a return to moderate growth on top of an expanded base.

2.2 Main features: trend, seasonal and irregular components

The STL decomposition of the log series separates this story into its constituent parts (Figure 2). The trend component captures the slow-moving backbone of the series. It begins at a relatively low level in 2000 and rises almost continuously over the 25-year window. There are noticeable bends around the two major crises. During the GFC the trend flattens and slightly dips, consistent with a period of stagnation or mild contraction. During the COVID-19 shock it experiences a sharper downward kink, followed by a quick resumption of growth, illustrating how severe but short-lived the pandemic shock was in level terms.

The seasonal component in the decomposition is remarkably regular. Quarter after quarter, the same pattern repeats: some quarters consistently sit above the trend, others below. This reflects the systematic timing of output within each year. For Bosnia and Herzegovina, the seasonal cycle is likely linked to the construction season, agricultural patterns and the timing of tourism flows. The amplitude of this seasonal component in logs appears broadly stable over time, which means that seasonal peaks and troughs represent roughly similar percentage deviations from the trend in the early 2000s and in the 2020s.

The irregular component is where the unexpected action resides. For most of the sample it oscillates around zero with relatively small amplitude, indicating that once we account for trend and seasonality, residual shocks are modest. However, there are episodes where the irregular series exhibits clusters of large positive or negative values. The period around the GFC shows a string of negative residuals as the economy slows more abruptly than would be predicted by a smooth trend. The pandemic years are marked by very large negative outliers, followed by positive ones as the economy rebounds. These residual spikes remind us that even well-behaved macroeconomic series can be hit by sudden, rare events that are difficult to foresee.

2.3 Seasonal diagnostics: patterns within the year

The seasonal plot of the log series (Figure 3) arranges the data by quarter, drawing a separate line for each calendar year. This representation makes the within-year pattern very clear. In Bosnia and Herzegovina, certain quarters tend to be systematically stronger.

Typically, the middle quarters of the year exhibit higher levels of real GDP than the first or last quarters, consistent with a combination of weather-dependent activities and tourism. Over time the lines shift upward as the economy grows, but their shape is surprisingly stable, indicating that the basic timing of seasonal strength and weakness has not changed dramatically.

The seasonal subseries plot (Figure 4) provides a complementary view by focusing on each quarter across years. For instance, plotting all first quarters from 2000 to 2025 reveals a gradual upward drift with some notable dips in crisis years, while plotting all third quarters shows the same trend at a higher level, confirming that third quarters are systematically stronger. These subseries plots also highlight years where the seasonal pattern is disrupted. The pandemic year stands out, with unusually low values in the normally strong quarters and a more jagged trajectory throughout the year.

Lag plots of the log series (Figure 5) further illuminate its internal dynamics. When plotting GDP in one quarter against GDP in the previous quarter, the points cluster tightly along a rising line, signalling strong persistence: a high level this quarter is usually followed by a high level next quarter. Using longer lags, such as four quarters, reveals the combination of trend and seasonality. The points tend to sit near a diagonal but with a banded structure corresponding to different seasons, again reflecting the regularity of the seasonal components.

When we repeat these diagnostics for the differenced log series, the focus shifts from levels to growth rates. Seasonal plots of growth show that some quarters tend to deliver higher or lower growth than others, although the seasonal structure is more muted than in the levels. Subseries plots of growth by quarter across years show episodes of particularly strong or weak growth, with the pandemic year again producing the most extreme deviations. Lag plots of growth indicate that serial correlation is weaker than in levels: large positive or negative growth in one quarter does not guarantee the same in the next, although some persistence and clustering of volatility remain.

2.4 Differenced series and their decomposition

The first differences of the log series approximate quarter-on-quarter growth rates. Once we plot these differenced series, the long-run upward trend disappears as expected. The resulting curve fluctuates around zero, with periods of relatively calm growth punctuated by sharp spikes.

In Figure 9, the original and seasonally adjusted growth series lie almost on top of each other for most of the sample, suggesting that seasonal effects in growth rates are modest. However, around crisis episodes the differences become more visible. During 2009 and 2010, growth turns negative for several quarters, and the seasonally adjusted series shows how deep the contraction was once regular intra-year patterns are removed. In 2020 the growth series records the largest negative value in the entire sample, followed a year later by one of the largest positive rebounds.

The STL decomposition of the differenced series in Figure 10 confirms that most of the remaining variation after differencing is irregular. The trend component in growth is close to zero for long stretches, hinting that the mean growth rate is relatively stable over medium horizons once we exclude crises. A small seasonal component persists, indicating that even growth rates can have systematic within-year regularities, but its amplitude is tiny compared with the irregular residuals.

These findings underscore two points that are important for practitioners. First, differencing, while useful, is not a full substitute for formal seasonal adjustment. Second, growth rates are dominated by short-term shocks, making them volatile and noisy indicators of underlying economic strength; the level and trend components provide a more reliable sense of long-term progress.

3. Economic outlook

What do these patterns imply for Bosnia and Herzegovina’s economic outlook as of mid-2025? The trend in log real GDP, even after the disruptions of the GFC and COVID-19, continues to slope upward. This suggests that the economy has managed to preserve and gradually expand its productive base, benefiting from integration with European markets, remittances and a slowly improving business environment. Recent data from international sources confirm moderate positive real growth in the years after the pandemic, albeit at rates lower than the dazzling catch-up of the early 2000s.

At the same time, the decompositions and diagnostic plots highlight vulnerabilities. The strong seasonal component indicates a structure of production that remains sensitive to the calendar, particularly in sectors like construction, tourism and some services. This means that disruptions which strike during peak seasons can be disproportionately damaging. The irregular component shows that crises can generate very large one-off shocks, and the history of the series contains at least two such episodes. In a world of heightened geopolitical and climate-related risks, the possibility of future shocks cannot be ruled out.

The growth-rate series suggests that, outside crisis periods, quarterly fluctuations are relatively contained, which is encouraging for macroeconomic stability. However, the clustering of large residuals during crises emphasises the importance of policy buffers. Sound public finances, robust banking supervision and effective social safety nets are essential to smoothing the impact of shocks on households and firms.

Overall, the graphs paint a picture of an economy that has moved beyond the volatile reconstruction phase of the early 2000s and has settled into a pattern of moderate, trend-driven growth. The pandemic shock was severe but temporary. As long as structural reforms continue and external conditions do not deteriorate dramatically, Bosnia and Herzegovina’s real GDP is likely to keep rising, though probably at a pace closer to that of a mature emerging economy than to a fast-growing convergence star.

4. Methodological appendix

This brief appendix summarises the key tools used in the analysis, without going into technical detail.

Graphical methods are the starting point. Plotting the series in logs over time reveals the broad pattern of growth, while overlaying the seasonally adjusted series clarifies how much of the quarter-to-quarter movement is due to recurring seasonal factors. Seasonal plots, subseries plots and lag plots provide additional insight into within-year patterns and persistence. They help distinguish structural features, such as regular seasonal highs and lows, from idiosyncratic noise or one-off shocks.

Transformations play a crucial role. Taking logarithms is appropriate when variance rises with the level of GDP, because it makes proportional changes comparable across time. If () is real GDP in quarter (), the transformed series is (). First differences () approximate quarter-on-quarter growth, and seasonal differences () approximate year-on-year growth. These differenced series remove much of the trend and some of the seasonal pattern, focusing attention on short-term dynamics.

Seasonal adjustment and decomposition are conducted using STL, which stands for Seasonal-Trend decomposition using Loess. In an additive representation, the observed series can be written as (), where () is the trend-cycle, () the seasonal component and () the irregular remainder. STL estimates these components by repeatedly smoothing the series with locally weighted regressions: one set of smoothers extracts the seasonal pattern across years, another extracts the trend over time, and whatever is left becomes the remainder. The method is flexible, can handle changing seasonal patterns, and is robust to outliers, which makes it well suited to exploratory work with macroeconomic time series.

Together, logs, differencing, STL decomposition and informative graphics provide a coherent framework for understanding the behaviour of Bosnia and Herzegovina’s real GDP over a long horizon.

References

Cleveland, R. B., Cleveland, W. S., McRae, J. E., & Terpenning, I. (1990). STL: A seasonal-trend decomposition procedure based on Loess. Journal of Official Statistics, 6(1), 3–73. https://www.math.unm.edu/~lil/Stat581/STL.pdf

Eurostat. (2025). National accounts and GDP – Statistics explained. European Commission. https://ec.europa.eu/eurostat/statistics-explained/index.php/National_accounts_and_GDP

Eurostat. (2024). Gross domestic product (GDP) and main components (output, expenditure and income), quarterly – Chain linked volumes, index 2020 = 100 (namq_10_gdp). Retrieved from Eurostat database.

Hyndman, R. J., & Athanasopoulos, G. (2025). Forecasting: Principles and practice (3rd ed.). OTexts. https://otexts.com/fpp3