Application of the Holt–Winters Model in the Forecasting of Passenger Traffic at Szczecin–Goleniów Airport (Poland)

Abstract

Accurate short-term passenger forecasts help regional airports align capacity with demand and plan investments effectively. Drawing on quarterly traffic data for 2010–2024 supplied by the Polish Civil Aviation Authority, this study employs Holt–Winters exponential smoothing to predict passenger volumes at Szczecin–Goleniów Airport for 2025. Additive and multiplicative formulations were parameterized with Excel Solver, using the mean absolute percentage error to identify the better-fitting model. The additive version captured both the steady post-pandemic recovery and pronounced seasonal peaks, indicating that passenger throughput is likely to rise modestly year on year, with the highest loads expected in the summer quarter and the lowest in early spring. These findings suggest the airport should anticipate continued growth and consider adjustments to terminal capacity, apron allocation, and staffing schedules to maintain service quality. Because the Holt–Winters method extrapolates historical patterns and does not incorporate external shocks—such as economic downturns, policy changes, or public health crises—its projections are most reliable over the short horizon examined and should be complemented by scenario-based analyses in future work. This study contributes to sustainable airport management by providing a reproducible, data-driven forecasting framework that can optimize resource allocation with minimal environmental impact.

1. Introduction

Today, air transport is the fastest-growing branch of transportation in the world [1], making it possible to reach almost any place on Earth in a day [2]. Thanks to its peculiar characteristics—speed of movement and high level of safety—it is the branch that is currently the most important in passenger transportation, especially over medium and long distances [3]. There is another feature of the air transport services market that can be pointed out as characteristic, and that is seasonality. In air passenger traffic, the peak of traffic is in the summer months, while, in cargo traffic, it is in March and October [4].

In the context of the growing global demand for transport, airports face a double challenge: adapting to increasing passenger traffic while meeting the requirements of national and international sustainable development strategies, which impose restrictions on operators in areas such as energy consumption and noise emissions. For this reason, airports, including Szczecin–Goleniów Airport, should implement forecasting tools that will not only predict future traffic volumes but also contribute to the implementation of sustainable development concepts. However, it should be borne in mind that sustainable development is not only about pro-environmental measures, but also about social aspects. Increasing awareness and enriching societies contributes to greater mobility of people for educational, professional, and recreational purposes. In this respect, this study and other future forecasts may contribute to improvements in passenger service at airport terminals by reducing waiting times at check-in, security control, and boarding. Based on forecasts, airport managers can take action in advance to meet future demand. Therefore, it can be concluded that forecasting future airport traffic contributes not only to the fulfillment of environmental requirements, but also to social requirements by shortening and improving the passenger service process at airports.

This article focuses on passenger transport at Szczecin–Goleniów Airport, located in northern Poland, in the West Pomeranian Voivodeship. The aim of the research was to calculate a forecast of the number of passengers carried for 2025 using the Holt–Winters method, considering the cumulative number of passengers arriving and departing from the studied airport. The adopted method is widely used to calculate forecasts for phenomena characterized by seasonality. The quarterly traffic statistics of the Szczecin–Goleniów Airport for the years of 2010–2024, developed and made available by the Civil Aviation Authority, were used as a starting point for the calculations.

The forecasts carried out allowed to indicate a growing trend in passenger traffic at Szczecin–Goleniów Airport. The forecast indicates that, in 2025, the Szczecin–Goleniów Airport will handle 3.75% more passengers than in 2024.

The study presented in this paper can serve as a guideline for the Szczecin–Goleniów Airport and other regional airports with a similar business profile. Knowing the approximate future number of passengers allows the analysis of current and future capacity and planning of infrastructure investments to meet future demand. The increasing number of passengers at airports also has environmental implications. Knowing the approximate future number of passengers makes it possible to forecast future energy consumption, noise emissions, or waste production. It can also enable more efficient flight scheduling, of which there are more and more as demand grows. All of this can contribute to sustainable environmental planning at airports in the long term.

However, it should be noted that the Holt–Winters method is not without limitations. Firstly, it only allows short- and medium-term forecasting, and the calculated forecasts do not take into account random events such as pandemics or armed conflicts.

2. Literature Review

Publications are available that take a broad view of the theory and practice of air transport management [5]. However, most studies focus on particular aspects of the aviation sector. Authors extensively discuss the impact of air transport on mobility in global [6] and regional [7] terms, also pointing out the close relationship between the development of the air transport sector and the economic growth of individual countries and regions [8,9,10]. The authors also analyze the impact of the aviation sector on tourism development [11,12] and passenger perception of air services [13]. After 2020, the issue of air transport resilience to disruptions from the environment has also emerged [14]. Of relevance in this context is the COVID-19 pandemic, which affected not only air transport and caused a drastic decline in traffic [15,16,17], but also affected the entire global economy.

In addition to issues related to the operation of the entire air transport sector, airports are a separate issue. One of the issues analyzed is the impact of airport operations on the development of transportation systems in the region [18,19]. The quality of services at airports and related passenger expectations and satisfaction levels are also a topic of studies [20,21,22,23]. The COVID-19 pandemic has also affected the operation of airports [24]; so, as with the industry as a whole, authors have begun to study their flexibility in the context of changes in the environment [25]. However, from the point of view of this publication, the most important issue is the capacity and throughput of airports, taking into account passenger streams, which is the subject of numerous scientific studies [26,27,28,29,30,31]. Numerous authors also attempt to predict future traffic at airports and model passenger flows in Europe and around the world [32,33,34,35,36,37].

Analyzing the subject of Polish airports, it can be seen that they are the subject of numerous scientific studies covering a wide range of issues. Authors discuss the topic of sustainability from environmental [38,39] and social [40] perspectives, as well as the economic situation of airports during a period of stability [41] and during the COVID-19 pandemic [42]. The development of Polish airports in the widest sense is also the subject of scientific studies, both from the architectural and urban planning sides [43] and in organizational aspects resulting from user needs [44,45].

The Holt–Winters method is a popular tool used in research studies to calculate forecasts in various transportation sectors, including, but not limited to:

• Rail transportation [46,47];
• Urban public transportation [48,49];
• Air transportation [50,51,52,53].

This article focuses on the use of the Holt–Winters method in passenger traffic forecasting. However, it is not the only tool that can be used for this purpose. In other studies, authors use the Parallel Hybrid Biobjective Generic Algorithm [54] and multi-objective linear programming [55] for optimizing urban pedestrian traffic. Studies also include forecasts of pedal-driven commuting and foot traffic in cities using deep learning approaches [56] and neural networks [57]. Other methods of forecasting presented in studies are, for example, deep learning [58], time series methods [59] or video-based traffic forecasting [60]. Each of these methods fulfils its purpose and allows future traffic volumes to be calculated or estimated with some accuracy. The combination of different methods within a single study allows for an increase in the accuracy of the study and thus increase the accuracy of the forecasts.

The literature to date on air transport is extensive and diverse. Numerous works present both the theory and practice of air transport management, focusing on, among others:

• The impact of aviation on mobility and economic development—global and regional analyses indicate that the growth of the aviation sector correlates strongly with the economic growth of countries and regions.
• Links to tourism and passenger perception—studies highlight how aviation services shape tourism traffic and traveler expectations.
• Resilience of the sector to disruption—post-2020, there has been considerable work analyzing the impact of the COVID-19 pandemic on aviation and the global economy.

At the airport level, researchers are focusing on:

• The role of airports in the development of regional transport systems;
• Quality of service and passenger satisfaction;
• Operational flexibility in the face of changes in the environment (e.g., COVID-19);
• Capacity and operational capability of airports and modelling of passenger flows, including traffic forecasting in Europe and worldwide.

Polish airports are, in turn, analyzed in terms of:

• Sustainability (environmental and social aspects);
• Economic condition in stable and crisis periods;
• Infrastructural development and organizational adaptation to user needs.

Despite the wealth of research, there is a lack of studies forecasting the volume of passenger traffic at Polish airports, in particular using the Holt–Winters method. Filling this gap is important both for airport managers and for decision-makers planning the development of airport infrastructure and services. This article addresses this issue by offering model traffic forecasts for one of Poland’s regional airports using the Holt–Winters method, and thus, contributes to the national and international literature on the subject.

3. Materials and Methods

3.1. Research Subject

The Szczecin–Goleniow Airport is a regional airport, located in northern Poland, in the Zachodniopomorskie Voivodeship (Figure 1). The Szczecin–Goleniów Airport was established in 1954/55, originally as a military airport, with civilian traffic also introduced in 1967. Originally, commercial flights were only operated by the national carrier LOT Polish Airlines on domestic routes to Warsaw, Gdańsk, Katowice, and Kraków. Over the years, the airport has undergone numerous modernizations of the apron, terminal buildings, and security infrastructure. Between 2004 and 2006, Terminal C was modernized, increasing the airport’s capacity to between 550,000 and 600,000 passengers per year. The facility was designed to simultaneously handle two aircrafts with a capacity of up to 76 passengers each. Between 2012 and 2015, the aircraft maneuvering area was expanded and the aprons were extended and upgraded, allowing the simultaneous handling of two C-class aircrafts (for example, a Boeing 737-700 or Airbus A320) or one D-class aircraft (for example, a Boeing 767 or Airbus A300) [61]. The latest upgrade did not include the terminal building; so, the capacity of the airport on the ground side has not changed [62].

Currently, the airport handles domestic and international traffic, including traffic outside the Schengen zone. According to estimates, the airport covers a population of about 1.6 million. The airport has a runway measuring 2500 m in length and 60 m in width, and aprons with areas of 17,500 m², 28,500 m², 9500 m², and 11,000 m². The passenger terminal has an area of 2,600 m² and two separate arrival halls (Schengen and non-Schengen), allowing up to 500 passengers per hour to check in. The port has six parking stands for a category C aircraft, that is, an aircraft with a wingspan of 24 to 36 m and a landing gear wheelbase of between 6 and 9 m. This category includes the most popular aircrafts in operation—Boeing 737 and Airbus A320 [61]. The distance of the airport from Goleniów is about 5 km, while, from Szczecin, it is 24 km in a straight line (about 40 km by public roads). There is also a railroad leading to the airport, serving connections from Szczecin and Kolobrzeg.

The dominant segment of traffic at Goleniów Airport remains that carried by low-cost carriers. On a multi-year basis, it can be noted that, over the past ten years, the number of passengers served has presented an upward trend—with the exception of 2020 and 2021, the period of the COVID-19 pandemic (Figure 2). Now, in the post-pandemic period, an increase in the number of passengers served is again visible, while it has not yet reached the pre-pandemic level.

The route network of Szczecin–Goleniów Airport focuses on internal flights and revenue destinations. During the summer season, it is supplemented by single charter flights to popular resorts in Europe, Asia, and North Africa.

Table 1. Flights operated from Szczecin–Goleniów Airport.

Carrier	2023	2024	2025
LOT	Warsaw	Warsaw	Warsaw
Ryanair	Warsaw Krakow London Liverpool Dublin	Krakow London Liverpool Dublin	Krakow London Liverpool Dublin
Norwegian	Oslo	Oslo	X
Wizzair	Oslo	Oslo	Oslo
EnterAir	Burgas Antalya	X	X
Ryanair Sun	X	Antalya	Antalya
SkyUp Airlines	X	X	Marsa Alam

Source: our own elaboration based on [62].

shows the destinations to which flights were operated from Szczecin–Goleniów Airport in 2023–2025, along with the carriers serving them.

In summary, Szczecin–Goleniów Airport is a regional airport that handles over 300,000 passengers annually and is experiencing year-on-year growth, excluding the COVID-19 pandemic period. Therefore, an awareness of the approximate future passenger traffic at the airport can help managers make future decisions regarding the expansion and modernization of the terminal in order to adapt its capacity to growing demand.

What is more, another terminal upgrade is planned for 2024–2027. The new building is to have 17,000 square meters of floor space, and its capacity is expected to increase to more than triple of its current state [64]. Such a fact led to the selection of Szczecin–Goleniów Airport as the subject of this study. From the decision-makers’ point of view, it is important to know how future traffic flows will develop and over what period further investments will be necessary.

3.2. Research Method

The Holt–Winters method was used for forecasting. This method is used when the time series is characterized by seasonal and random fluctuations and when it contains a development trend. We can distinguish its two forms—the additive and multiplicative model [65]. As Wilson and Allison-Koerber point out, this method is advisable with a minimum of 4–5 observations per season and a short to medium forecast horizon [66]. The choice of variance is related to the nature of seasonality. The additive model assumes that seasonal fluctuations have a constant amplitude regardless of the level of the series, while the multiplicative model assumes that the amplitude changes in proportion to the level. In data where there are periods with very small values (e.g., Q2 2020 during a pandemic), the proportionality assumption leads to instability (dividing by values close to zero).

Data on passenger traffic at Goleniów Airport were downloaded to MS Excel from the Civil Aviation Authority website. The calculations were performed separately for the additive and multiplicative models. For both models, the file contains the following columns: year, quarter, period, variable level, trend coefficient, seasonal component, forecast, and average absolute percentage forecast error.

In the first step, three smoothing constants were calculated, namely:

• Level of the variable at time t (1) and (2):

$$\mathrm{additive}: F_t=\alpha \left(Y_t-C_{t-r}\right)+\left(1-\alpha \right)\left(F_{t-1}+S_{t-1}\right)$$

(1)

$$\mathrm{multiplicative}: F_t=\alpha \left(Y_t/C_{t-r}\right)+\left(1-\alpha \right)\left(F_{t-1}+S_{t-1}\right)$$

(2)

• Trend coefficient at time t (3):

$$\mathrm{additive}, \mathrm{multiplicative}: S_t=\beta \left(F_t-F_{t-1}\right)+(1-\beta )S_{t-1}$$

(3)

• Seasonal component at time t (4) and (5):

$$\mathrm{additive}: C_t=\gamma \left(Y_t-F_t\right)+(1-\gamma )C_{t-r}$$

(4)

$$\mathrm{multiplicative}: C_t=\gamma \left(Y_t/F_t\right)+(1-\gamma )C_{t-r}$$

(5)

where α, γ, and δ are smoothing parameters ranging from 0 to 1; r is the length of the seasonal cycle (the number of cycle phases)$; Y_t$ are the data values; and t is the value of consecutive periods (1, 2, ..., n) [67]. The data in this study are presented on a quarterly basis; therefore, the value of the variable r was taken as 4. By definition, the smoothing parameter is the number of consecutive expressions, i.e., values of the variable, taken to determine a single moving average value [67].

Next, using the previously obtained smoothing parameters, forecasts were calculated. The forecast equation for t ≤ n, where n is the number of words in the time series of the forecast variable, takes the forms (6) and (7) [68]:

$$\mathrm{additive}: Y_t^{*}=F_{t-1}+S_{t-1}+C_{t-1}$$

(6)

$$\mathrm{multiplicative}: Y_t^{*}={(F}_{t-1}+S_{t-1})C_{t-1}$$

(7)

On the other hand, the forecast equation for t > n is as follows in (8) and (9):

$$\mathrm{additive}: Y_t^{*}=F_n+(t-n)S_n+C_{t-1}$$

(8)

$$\mathrm{multiplicative}: Y_t^{*}={(F}_n+(t-n)S_n)C_{t-1}$$

(9)

The forecast results were used to examine the forecast error. When analyzing time series, a number of ex-post-forecast error measures are used. Ex-post-forecast errors are statistics used to subsequently assess forecasting accuracy. They are the results of comparing past forecasts with the already known true values of the forecast quantities. In this study, in order to examine the accuracy of forecasts for each model, the forecasts were evaluated using the mean absolute percentage error (MAPE) (10). This error eliminates the phenomenon in which positive deviations of empirical values from theoretical values are offset by negative deviations [69].

$$MAPE={\displaystyle \frac{1}{n}}\sum _{t=1}^n\left|{\displaystyle \frac{Y_t-Y_t^{*}}{Y_t}}\right|·100\%$$

(10)

The final step was to use the Solver add-in to determine the optimal forecast, i.e., the one with the lowest forecast error. The forecast error was minimized by changing the smoothing constants using the GRG (Generalized Reduced Gradient) nonlinear method, while maintaining the values of the coefficients α, β, γ ∈ [0,1]. The nonlinear GRG method is tailored to the problems of nonlinear methods and occurs as a feature of the add-on Solver.

The Holt–Winters method is suitable for forecasting data characterized by three features: seasonality, trendiness, and equal intervals between successive available data (for example, monthly, quarterly, annual, etc., intervals). Therefore, the Holt–Winters method is suitable for forecasting air passenger traffic, as it is characterized by seasonality, that is, cycles visible as fluctuations at specific times. Moreover, the data show a trend, by which we can see whether the values maintain an upward or downward tendency. Usually, aviation statistics are presented in months or quarters, which allows the number of phases of a seasonal cycle to be determined smoothly. The larger time span of the data makes it possible to generate an optimal forecast.

The statistical analyses were complemented by a scenario method, specifically scenarios of ambient states. This method consists of four steps:

• Stage 1—identification of the enterprise’s macro-environment and competitive environment and the factors that have a key impact on the enterprise’s performance.
• Stage 2—evaluation of the identified factors in terms of:
  • The strength and direction of a factor’s impact on the organization on a scale from −5 (greatest negative impact) to +5 (greatest positive impact);
  • The likelihood of each factor occurring in three trends: upward, downward, and stabilizing.
• Stage 3—rank the trends according to four scenarios: optimistic (trends with the greatest positive impact on the business), pessimistic (trends with the greatest negative impact on the business), most likely (trends with the highest probability of occurrence, regardless of strength and direction of impact), and surprise (trends with the lowest probability of occurrence, regardless of strength and direction of impact).
  Stage 4—calculations to determine the average strength of impact of each factor in each scenario.

The assessment of the potential impact of individual factors and the likelihood of their occurrence is made based on the knowledge and experience of the persons developing the scenario. The development of scenarios of ambient states allows the organization’s environment to be assessed in terms of its stability or instability and the level of structuring [70].

3.3. Results

Data on the number of passengers served in domestic and international traffic—, scheduled and chartered at Goleniow Airport (Poland) in successive quarters of the years of 2010–2024, were obtained from the website of the Civil Aviation Authority [71] (

Table 2. Passenger served at Goleniow airport in successive quarters of the years of 2010–2024.

Time		Passengers	Time		Passengers	Time		Passengers
2010	I	48,638	2015	I	69,122	2020	I	92,139
	II	57,341		II	109,906		II	6144
	III	101,549		III	134,345		III	64,279
	IV	61,035		IV	98,789		IV	23,286
2011	I	48,580	2016	I	92,264	2021	I	11,917
	II	64,092		II	128,660		II	24,829
	III	80,284		III	136,496		III	78,049
	IV	65,261		IV	110,017		IV	67,054
2012	I	55,980	2017	I	106,727	2022	I	59,076
	II	113,339		II	157,191		II	111,972
	III	110,227		III	172,760		III	144,374
	IV	67,517		IV	141,842		IV	104,450
2013	I	58,555	2018	I	124,587	2023	I	93,032
	II	89,260		II	158,369		II	129,888
	III	107,678		III	179,539		III	158,249
	IV	66,841		IV	136,168		IV	96,295
2014	I	54,103	2019	I	120,055	2024	I	85,516
	II	75,784		II	146,609		II	127,955
	III	93,831		III	166,468		III	145,810
	IV	62,659		IV	147,347		IV	119,838

Source: our own elaboration based on [71].

) and then sorted, and their statistical analysis was performed (

Table 3. Results of statistical analysis of served passengers at Goleniow airport in 2010–2024.

Period	Minimum Value	Maximum Value	Average	Standard Deviation	1st Quartile	Median Value	3rd Quartile	Coefficient of Variation
2010–2024	6144	179,539	97,733	41,175	65,016	97,542	128,967	42.13%

Source: our own elaboration.

).

The analysis indicated that an average of 97,733 passengers were served per quarter in the years under study. The least number of passengers served was 6144 in the second quarter of 2020, and the most was 179,539 in the third quarter of 2018. Half of the quarters surveyed had a number of passengers greater than 97,542, and half had a number of passengers less than a given number. In addition, the coefficient of variation of 42.13% indicates average variability. It should be noted that 2020 brought large declines in traffic due to the COVID-19 pandemic, which were as much as 67.98% lower compared to the previous year. The bad streak continued in 2021, where 68.67% fewer passengers were served than in 2019.

By visualizing the data with a graph, it was possible to determine that it is characterized by an increasing trend (Figure 3), as well as seasonality (Figure 4). The trend is discernible from 2010 to Q3 2019, where a further decline was caused by the aforementioned COVID-19 pandemic. An upward trend can be seen in Q1–Q3 2010, followed by a downward trend from Q4 2010 to Q1 2021. These factors determined the use of the Holt–Winters exponential smoothing method, an additive and multiplicative model, to create a passenger forecast for 2025.

The results of the forecast for 2025 for both models, including the smoothing coefficients, are shown in

Table 4. Forecast results for 2025.

Specification		Model
		Additive	Multiplicative
The result of the 2025 forecast	Quarter I	106,733	94,189
	Quarter II	114,926	107,044
	Quarter III	158,198	165,279
	Quarter IV	117,246	114,711
Smoothing factor	α	0.9991	0.7224
	β	0	0
	γ	0.5972	0.2281

Source: our own elaboration.

and by means of Figure 5 and Figure 6. The optimal values of the coefficients were selected using the MS Excel Solver add-on by minimizing the value of the average absolute error of the MAPE forecast, taking into account the values of the coefficients α,β,γ∈ [0,1]. The parameter grid was viewed with an accuracy of 0.0001. The number of phases of the seasonal cycle was taken as shown in Table 4.

The best performance of the Holt–Winters method occurred in the additive model, and Figure 3 shows a good fit between data and forecasts. The lack of an upward fluctuation amplitude was also in favor of the additive model. The used model also achieved a lower value of forecast MAPE of 43.70%, but it was 54.84% in the multiplicative model. As defined by Asrah et al. [72], a MAPE value of 20–50% can be described as a reasonable forecast. In addition, the values close to zero in 2020 cause the seasonal factor in the multiplicative model to reach extremely high or low values, which amplifies forecast errors and leads to the oscillation of the forecast path. In the additive model, the magnitude of the disturbance is limited because the seasonal component is added rather than multiplied.

The forecast for 2025 was 497,103 passengers and an average of 124,276 passengers per quarter. As shown by the statistical analysis presented in

Table 5. Results of the statistical analysis of passengers served at Goleniów airport in 2025.

Period	Minimum Value	Maximum Value	Average	Standard Deviation	1st Quartile	Median Value	3rd Quartile	Coefficient of Variation
2025	106,733	158,198	124,276	23,060	111,526	116,086	142,247	18.56%

Source: our own elaboration.

, the lowest number of passengers will be handled in the first quarter, and the highest in the third quarter. Half of the surveyed quarters have a number of passengers greater than 116,086, and half have a number of passengers less than a given number. In addition, the coefficient of variation of 18.56% indicates a small dispersion of data values.

The development of the scenarios of ambient states began with the identification of the factors having the greatest impact on the operations of Szczecin–Goleniów Airport. Each factor was then assessed in terms of the strength of influence and direction of impact, as well as likelihood of occurrence [

Table 6. Factors influencing the operation of Szczecin–Goleniów Airport.

Factor	Trend	Strength of Impact	Probability of Occurrence
GDP per capita level	Growth	+4	0.6
	Stabilization	+1	0.3
	Regression	−3	0.1
Inflation	Growth	−3	0.4
	Stabilization	+2	0.4
	Regression	+4	0.2
Ticket prices	Increase	−3	0.6
	Stabilization	+1	0.3
	Regression	+5	0.1
International conflicts	Growth	−5	0.2
	Stabilization	−1	0.3
	Regression	+5	0.5
Environmental requirements	Growth	−4	0.7
	Stabilization	−1	0.2
	Regression	+2	0.1
Offer of travel destinations	Growth	+5	0.2
	Stabilization	−1	0.6
	Regression	−5	0.2
Level of wealth of society	Growth	+5	0.3
	Stabilization	+3	0.2
	Regression	−4	0.5
Airport access	Increase	+4	0.7
	Stabilization	−1	0.2
	Regression	−3	0.1
Offer of competing airports	Growth	−4	0.5
	Stabilization	−1	0.3
	Regression	+4	0.2

Source: our own elaboration.

]. The analysis and assessment were based on the authors’ knowledge and experience and online sources and data originating from Eurostat, Airports Council International Europe, International Air Transport Association, International Civil Aviation Organization, and Eurocontrol.

Based on the information in Table 6, four scenarios of ambient states were constructed—optimistic (

Table 7. Optimistic scenario.

Factor	Strength of Impact
GDP per capita level	+4
Inflation	+4
Ticket prices	+5
International conflicts	+5
Environmental requirements	+2
Offer of travel destinations	+5
Level of affluence of society	+5
Airport access	+4
Offer of competing airports	+4
Average impact:	+4.22

Source: our own elaboration.

), pessimistic (

Table 8. Pessimistic scenario.

Factor	Strength of Impact
GDP per capita level	−3
Inflation	−3
Ticket prices	−3
International conflicts	−5
Environmental requirements	−4
Offer of travel destinations	−5
Level of affluence of society	−4
Airport access	−3
The offer of competing airports	−4
Average impact:	−3.77

Source: our own elaboration.

), most likely (

Table 9. Most likely scenario.

Factor	Positive Force of Impact	Negative Force of Impact	Likelihood of Occurrence
GDP per capita level	+4		0.6
Inflation	+2	−3	0.4
Ticket prices		−3	0.6
International conflicts	+5		0.5
Environmental requirements		−4	0.7
Offer of travel destinations		−1	0.6
Level of affluence of the population		−4	0.4
Access to the airport	+4		0.7
Offer of competing airports		−4	0.5
Average impact:	+3.75	−3.16

Source: our own elaboration.

), and surprise (

Table 10. Surprise scenario.

Factor	Positive Force of Impact	Negative Strength of Impact	Probability of Occurrence
GDP per capita level		−3	0.1
Inflation	+4		0.2
Ticket prices	+5		0.1
International conflicts		−5	0.2
Environmental requirements	+2		0.1
Offer of travel destinations	+5	−5	0.2
Level of affluence of society	+3		0.2
Access to the airport		−3	0.1
Offer of competing airports	+4		0.2
Average impact:	+3.83	−4.00

Source: our own elaboration.

).

In the accelerated growth scenario, the macroeconomic environment is favorable for mobility: The region’s real GDP grows, inflation stabilizes at around 3%, and competition from low-cost carriers and cheaper sustainable aviation fuels (SAFs) make tickets cheaper in real terms. Geopolitical risks decline, and the EU eases the ETS burden on small ports. In such an environment, the strength of key factors averages +4.22 points, which translates into a dynamic demand trajectory: about 570,000 passengers in 2025, 700,000 in 2027, 950,000 in 2030, and 1.25 million in 2035 or 74% of the new terminal’s capacity (1.7 million pax/year) planned for 2027. Early warning indicators will be LCC slot bookings exceeding 80%, an average fill rate above 90% during the summer peak, and accelerated investments in Poznan and Gdansk. Management should accelerate the second phase of terminal expansion, intensively solicit hub routes, and expand multimodal offerings (rail + parking) to take advantage of the growth window and protect against crowding effects.

In the negative version, the global environment deteriorates: Europe falls into recession in 2026–27, energy inflation increases ticket prices, armed conflict in the East escalates, and the EU tightens environmental requirements without shielding regional ports. Ryanair and Wizz Air reduce offerings in Poland. The cumulative average impact is −3.77 points, and traffic drops to 400,000 pax in 2025, to reach only 380,000 in 2027 and 550,000 in 2035 (32% of capacity). Early warning signs will be cancellations of more than 8% of operations, a load-factor below 75%, and an additional fuel surcharge of more than EUR 12 per segment. In such a situation, the airport should phase out terminal expansion, develop cargo operations and retail space, and offer selective incentives to niche carriers operating smaller regional jets.

The most likely path assumes a moderate economy: The region’s GDP grows, inflation gradually declines to 3–4%, and ticket prices rise moderately along with ETS and fuel costs. The average positive strength of the factors is +3.75 points, and negative—3.16 points. The Holt–Winters’ forecast for 2025 (497,103 passengers) becomes the benchmark, with the port reaching 570,000 pax in 2027, 700,000 in 2030, and 900,000 in 2035, about half the terminal’s capacity. Critical alerts are a decline in rail’s share of port access, an increase in the no-show rate above, or a sudden exodus of traditional carriers. Priorities include digitizing processes (sel-bag drop; e-gate), marketing city breaks to Scandinavia and the Mediterranean, and partnerships with tour operators to extend the charter season. Such measures will maintain a comfortable capacity reserve and gradually increase non-aero revenues.

The last scenario involves alternating demand impulses and supply shocks: major sporting events (e.g., EURO 2028) alternate with a sudden health crisis or cyberattack; oil prices jump between USD 50 and USD 130 per barrel; and EU climate policy changes from term to term. The average positive impact of the factors is +3.83 points and negative impact is 4.00 points, generating a wide range of traffic: 430–580,000 pax in 2025, 400–750,000 in 2027, and up to 600–1,300,000 in 2035. Indicators of risk are quarterly passenger deviations from plan in excess of ±10%, abrupt changes in LCC schedules with less than 60 days’ notice, and WHO alerts. To operate in such a turbulent environment, the port should implement a capacity-on-demand concept of flexible check-in areas and swing gates, maintain a cash reserve for a minimum of six months of operating costs, and negotiate SLAs with handling companies based on availability and short response times.

4. Discussion and Conclusions

This paper proposes the use of the Holt–Winters method to create a forecast of the number of passengers to be served for the next quarters of 2025 at Szczecin–Goleniów Airport. The study showed that a better-fitting forecasting model for the data studied is the additive model, which showed a lower MAPE value. The analysis of seasonal variance showed that, since 2010, the spread of quarterly deviations around the trend has varied at most ±30 thousand pax, regardless of the size of the trend. Such ‘flat’ seasonality is correctly described by the additive model. The multiplicative model overestimates fluctuations in high traffic years and underestimates them in low demand years. In addition, the additive model is a better fit for data characterized by a linear trend, which is what occurred in the study, while the multiplicative model is better suited for data with an exponential trend. As a result of the calculations, the number of passengers forecast for 2025 was set at 497,103, which is 3.75% higher than in 2024. It should also be noted that the forecast value is affected by data from 2020–2021, when the COVID-19 pandemic progressed, generating a significant reduction in the number of passengers served. The occurrence of such unusual phenomena affects the quality of further forecasts. It should be noted that the forecasts developed using the Holt–Winters method are a linear projection of previous years’ data; so, they are unable to take into account future disruptions and random events affecting the operation of the industry as a whole. This therefore represents a significant limitation for the research. Once the forecast phenomena have occurred, it is possible to validate the forecast by comparing its results with actual observational data to assess the quality of the forecast. The COVID-19 pandemic and any other causes of extreme data fluctuations can significantly affect the forecast and lead to problems with the components of the Holt–Winters model, i.e., the level of the variables, trend, and seasonality. Changes in data structure can result in long-term forecast distortions. Meanwhile, the quality of the forecast is also affected by the amount of input data used for estimation. A longer data interval influences the more accurate identification of trend and seasonality patterns, i.e., a better smoothing of the forecast. The use of model optimization, or in the case of this article, the use of the Solver add-on, by calibrating the model parameters, offsets the resulting distortions to some extent and balances the sensitivity to observations.

The achieved error rate is largely due to data fluctuations and the change in data structure from the COVID-19 pandemic period. Any unforeseen random events affect the accuracy of the forecast. The destabilization of the trend and seasonality during this period causes the forecast error to increase. In addition, if the forecast was made for a longer period, one can expect an increased risk of error accumulation. Thus, when interpreting both the result of the forecast and the forecast error, it is necessary to take into account the context of the analyzed phenomenon, as well as to identify possible sources of error.

As mentioned earlier, the paper used MAPE to evaluate the indicators to determine the optimal predictive model. In contrast, Cheng-Hong Yang and other authors in their papers used the Holt–Winters additive model for selected airports comparing it with other methods and used three errors to evaluate the prediction: mean absolute percentage error, mean absolute error (MAE), and root mean squared error (RMSE) [73]. The resulting MAE for the method had the lowest value for passenger traffic for Paris-Charles de Gaulle Airport and Shanghai Pudong International Airport compared to the other methods.

The use of some data processing variants replacing the atypical data from the COVID-19 pandemic (Q2 2020–Q2 2021) can also be adopted for further consideration. Among these is seasonal imputation, i.e., replacing the extreme quarters by the average of the corresponding quarters of 2015–2019. Another is segmented modelling with separate Holt–Winters estimation for the sub-sections of 2010–2019 and 2022–2024, followed by forecast stitching. A dummy variable could also be used for the quarters Q2 2020–Q2 2021 in the level component.

Although the Holt–Winters model is effective for short-term forecasts, it may be less accurate for long-term forecasts. For long-term forecasts, trend and seasonality values may become less stable, affecting forecast accuracy. A larger range of data and finding optimal coefficients also account for the accuracy of forecasts. Narrowing the values of smoothing coefficients to α, β, γ∈ [0,1] may seem to be an unnecessary constraint. The best forecasts may arise regardless of the constraints on the values of the smoothing coefficients. Further considerations may include calculations without narrowing the parameters. Some of the factors can affect the seasonality of the data such as changes in holiday destinations. The method does not take into account such phenomena as a decline in customer income and better offerings from other airports, which can cause changes in passenger ventures. Emergencies like the outbreak of wars or economic crisis can weaken the quality of the forecast by not reacting quickly to the change and will not quickly register a lower value of the forecast based on past elements. Also, when there is a good economy and its recovery, the model will not respond immediately.

Importantly, the method does not take into account economic factors and data on the economic environment affecting the predictions. These include ticket prices, destinations, airport access, the offer of competing airports, the value of gross domestic product (GDP), the unemployment rate, etc. These are also region-specific factors, and their incidence and impact may vary depending on the airport under study. Al-Sultan Ahmad and others also note the need to include gross domestic product (GDP), unemployment rate, ticket price, and other economic information in forecasts [53]. Further research can take these factors into account.

The Holt–Winters method only takes into account statistics from previous years, without considering factors from the environment and their impact on the company. A scenario analysis using scenarios of ambient states made it possible to define the most important factors and their impact on the operations of Szczecin–Goleniów Airport by analyzing individual factors:

• GDP per capita/wealth—each 1 percentage point increase in real GDP per capita translates (historically) into an increase in regional airport traffic of around 1.2%; therefore, positive macroeconomic scenarios almost linearly increase demand.
• Inflation and ticket prices—higher inflation reduces traffic twice over: it reduces real income and raises line costs (fuel, environmental charges).
• International conflicts—the airport mainly handles point-to-point traffic to Western Europe; however, escalating conflicts can reduce emigration and tourism demand by up to 10%.
• Environmental requirements—the introduction of SAF/ETS will increase the CASK (Cost per Available Seat Kilometer) of the line by EUR 1–3 per passenger; for EUR 70–100 tickets, price elasticity is high, which is a significant risk factor in the pessimistic scenario.
• Destination offer—each new scheduled route brings an average of 25–30,000 additional pax per year; priority is given to revenue destinations for the Polish diaspora and city breaks.
• Access to the airport—shortening the Szczecin airport rail commute to 25 min raises the rail share in the modal split from 5% to about 15%, which translates into about a 5% increase in total traffic.
• Port competition—the launch of CPK in the second half of the 2030s may draw away transfer traffic, but simultaneously take pressure off slots at WAW, which is an opportunity for Goleniów in the charter segment.

The analyses carried out can serve as guidelines for the managers of Szczecin−Goleniów Airport and other regional airports in Poland and Europe. Different scenarios of the economic situation indicate different possible directions of development. Recommendations for airport managers focus on actions in five areas, regardless of the scenario considered: infrastructure, route network, non-aero revenue, sustainability, and operational resilience (

Table 11. Recommendations for airport managers.

Area	Actions
Infrastructure	Maintain flexibility in the design of the new terminal (easy modular expansion), prepare a CAPEX reserve plan in the case of a slowdown.
Route network	Continue discussions with low-cost carriers about routes to hubs and tourist destinations; conditional incentives for carriers.
Non-aero revenue	Develop retail and parking services; in the pessimistic scenario, increase the share of cargo and e-commerce logistics.
Sustainability	Implement photovoltaic installations with energy storage; prepare SAF and carbon footprint reporting, which will improve the negotiating position with the lines and authorities.
Operational resilience	Exercise emergency response procedures in the event of a pandemic or cyberattack; maintain a cash reserve for approximately 6 months of OPEX.

Source: our own elaboration.

).

The scenario analysis carried out as part of this study only considered the basic economic and other factors affecting airport operations. Future research will use the same method, but in a more elaborate version based on a survey of airport managers and users. Statistical studies using other forecasting methods are also planned, followed by a comparative analysis of the results obtained.

Nevertheless, based on the forecast, a further upward trend in the number of passengers served at Szczecin–Goleniów Airport can be indicated, which is also in line with trends for the entire aviation industry. This is mainly due to the growing awareness and wealth of the population and the popularity of foreign travel for work, education, and leisure. If the forecasts indicate an upward trend, this is a signal for airports to take measures to adapt to the growing demand for transport and to handle more passengers in terminals in the coming years. Taking action in advance will help avoid airport congestion in the future, both on the ground and in the air. Furthermore, by incorporating sustainability criteria—such as reducing the carbon footprint through optimized flight schedules—into future scenario analyses, this approach can support decision-making in line with global climate goals and contribute to reducing air pollution and noise emissions.

For this reason, the above analyses can serve as a kind of guideline and reference point for Szczecin–Goleniów Airport and other airports with a similar profile. The method used in this study is reproducible for data characterized by seasonality, trend, and equal intervals. At the same time, the method does not require a minimum dataset to be used, but the larger the range of data used in the calculations, the more accurate the forecasts will be. The above principles mean that the Holt–Winters method can be used by other researchers and decision-makers at airports and in regions. The forecasts allow for a certain degree of prediction of future air traffic at the airport and enable advance planning of measures to handle more passengers and flights while maintaining environmental standards.

The advantage of the Holt–Winters method is its versatility. Therefore, future studies may consider using this method to calculate future passenger traffic forecasts at other airports in Poland and the European Union, at the community or individual country level. Such an approach will allow for a comparison of the situations at individual airports and the development of common sustainable development strategies. In the longer term, the calculated forecasts can be compared with scenario methods that consider economic and environmental factors and then analyzed to see whether additional variables can be reflected in the future number of passengers served. What is more, the forecasts can also be used in practice in the long term, i.e., in terminal development planning, but also in day-to-day operations, by controlling the use of equipment and devices, air conditioning, and lighting, thus contributing to improving the energy balance.

In further research, the authors plan to expand the study to include methods that take into account more external factors affecting airport traffic and compare the effectiveness of different approaches. The methods that can be used are: SARIMA, LSTM, XGBoost, or Prophet. The Holt–Winters model, on the other hand, was treated as a baseline because it takes into account seasonality and trend, which is particularly noticeable for passenger traffic at the airport. It has low computational requirements and is not threatened by over-fitting of the learning data by limiting the parameters used.