Forecasting inbound tourist arrivals to Iran post-COVID-19 pandemic: a small data approach using grey models Open Access

Tourism is crucial for the economic development of numerous countries, including Iran. It serves as a significant source of revenue, contributing to gross domestic product GDP (Pérez-Romero et al., 2024), creating employment opportunities (Bolukoglu and Gozukucuk, 2023) and fostering cultural exchange (Chang and Zhang, 2024). Tourism encourages investment in infrastructure, such as transportation (Noshab Hussain, 2023) and accommodation (Kampo et al., 2024), which can have a lasting positive impact on the economy. The United Nations World Tourism Organization (UNWTO) highlights that tourism can drive inclusive development, reduce poverty and promote environmental sustainability when managed responsibly (UNWTO, 2023).

The COVID-19 pandemic has profoundly impacted global tourism, leading to unprecedented declines in international travel (Yang et al., 2021). Iran, like many other countries, has faced significant challenges in its tourism sector due to travel restrictions, health concerns, and economic downturns. As the world gradually recovers from the pandemic, understanding and forecasting the inflow of foreign tourists to Iran has become crucial for effective planning and revitalization of the tourism industry.

Forecasting in the tourism industry is essential for several reasons. Accurate forecasts enable governments and businesses to develop strategic plans that align with expected tourism demand, including infrastructure development, marketing strategies and investment in new attractions and services (Ma and Su, 2024). Forecasting helps in efficient allocation of resources, ensuring that the tourism sector can meet anticipated demand without overburdening existing infrastructure or underutilizing resources, leading to better management of hotels, transportation and tourist attractions (Bi et al., 2020). Additionally, reliable forecasts assist in risk management by identifying potential fluctuations in tourist arrivals and enabling the formulation of contingency plans (Zhang and Tian, 2022). Governments can use forecasts to design policies that promote sustainable tourism development (Yeoman et al., 2022), address seasonality issues (Boto-García and Pérez, 2023) and balance tourist inflow with environmental and social considerations (Wang et al., 2020).

Effective indicators in the tourism industry are criteria that can be used to evaluate the effects of changes in the tourism industry, including financial, communal, ecological and heritage-related dimensions (Hussain et al., 2023), precise forecasting of inbound tourist arrivals each year can aid in the development of essential infrastructure like hotels and transportation hubs (Ghalehkhondabi et al., 2019). The goal of tourism demand forecasting is to achieve an accurate estimate of the need for products or services, as effective planning for these offerings relies on understanding anticipated purchases or usage. Both short-term and long-term forecasts can support the necessary provisions for tourists (Ghalehkhondabi et al., 2019).

In the wake of COVID-19, the tourism industry has transformed significantly. Accurate forecasting of tourist arrivals is crucial for planning. However, few studies have used advanced grey forecasting models for Iran's tourism sector post-pandemic. Previous research focused on pre-pandemic conditions or used traditional models that may not capture the uncertainties introduced by COVID-19. This study fills this gap by applying and comparing grey forecasting models to forecast Iran's tourism demand more accurately.

Pre-pandemic tourism forecasting studies primarily relied on traditional statistical models, such as time series (Sakhuja et al., 2016), econometric (Carmona-Benítez et al., 2017), machine learning (Hewapathirana, 2023) and neural network (Sirimal Silva et al., 2019) models, which often assume stable patterns and abundant historical data. The COVID-19 pandemic has rendered previous historical data in the tourism industry invalid for forecasting future trends. The future of tourism recovery requires adaptive strategies. In post-crisis environments, traditional forecasting models often struggle with data limitations and unpredictable shifts in market behavior. In the post-pandemic era, the tourism industry faces significant challenges driven by small, inconsistent and often unreliable data. This instability affects not only tourism metrics but also key socioeconomic indicators like income levels, consumer confidence and mobility patterns. In such uncertain conditions, forecasting approaches that rely solely on data-driven methods without depending on external variables become essential. Univariate forecasting has emerged as a practical solution in this context, offering simplicity, efficiency and reliability in data-scarce environments. By analyzing historical patterns within a single variable, univariate models are especially effective in post-crisis recovery scenarios and in developing nations where access to comprehensive datasets and advanced tools is limited.

This study leverages grey forecasting models, which are specifically designed to handle uncertainty, incomplete data and small sample sizes. Their ability to extract meaningful patterns without requiring extensive datasets makes them particularly suited for analyzing data from disrupted periods such as 2020–2023, where decision-making must navigate both uncertainty and urgency. By employing grey forecasting models, this research aims to provide a more resilient and adaptable approach to understanding future trends in inbound tourist arrivals to Iran. The data analyzed consists of annual records of inbound tourist arrivals to Iran from 2020 to 2023, with forecasts generated for the years 2024–2026. Accordingly, the rest of the article is organized as follows: Section 2 provides the literature review. In this section, the literature on the COVID-19 pandemic and its impact on the tourism industry, and tourism forecasting is explained. In Section 3, the proposed methodology is defined and the results and analysis are presented in Section 4. Lastly, Section 5 and Section 6 contain the discussion and conclusions.

In this section, literature and related research are presented. To better structure the section, the literature review is divided into three subsections. First, the study reviews research on the COVID-19 pandemic and its impact on the tourism industry. Then, forecasting in tourism and related literature is presented. Finally, definitions of grey forecasting are explained.

The COVID-19 pandemic has significantly affected the international tourism sector, marking one of the most significant challenges the sector has faced in recent history. Analyzing statistics and reports from UNWTO and other international bodies reveals a drastic decline in international tourists across the globe (UNWTO, 2023). This downturn has been attributed to widespread travel restrictions, lockdowns and the overall uncertainty surrounding the pandemic. The effect has been a profound disruption in international travel flows, leading to significant economic losses for countries that heavily rely on tourism. Various research has been conducted on the COVID-19 pandemic and its impact on the tourism industry (Arshad et al., 2023; Viana-Lora et al., 2023; Yeoman, 2023; Wong et al., 2025; Lo Duca and Marchetti, 2024; Martínez et al., 2025).

Becken and Loehr (2023) analyze COVID-19 policy responses in Asia–Pacific tourism through four potential future scenarios, linking these to sustainability outcomes. A key strength of their work lies in aligning short-term recovery policies with long-term sustainable development goals, providing actionable insights for decision-makers. However, their use of a framework not specifically tailored to tourism may reduce precision. Despite this limitation, their study offers valuable guidance for fostering resilience and adaptability in the tourism sector. Dinh Vu et al. (2022) focus on the impact of COVID-19 on Vietnam's tourism and propose recovery strategies. Their analysis, which is supported by official data and interviews, enhances the reliability of the findings. Nonetheless, their reliance on nonparametric statistics limits the ability to conduct causal analyses, presenting a notable limitation. Matiza (2022) explores how the COVID-19 pandemic may influence post-crisis tourist behavior, with a specific emphasis on perceived risk. By drawing on previous health crises, the study forecasts heightened perceived risks and their potential impact on travel decisions. The article offers strategies like improved governance and marketing to mitigate these risks, but the reliance on past crises and the lack of detailed, immediate solutions are limitations. A study that employs a tourism-specific framework and utilizes real official post-COVID-19 data to forecast tourist arrivals can address the weaknesses of previous research, ensuring enhanced precision and reliability.

Tourism demand forecasting is a critical area of research that has garnered significant attention due to its importance for strategic planning and policy formulation in the tourism industry (Neshat et al., 2024). Accurate forecasts enable stakeholders to make informed decisions regarding marketing strategies, resource allocation and infrastructure development (Georgescu et al., 2024). Various forecasting models have been used to forecast the tourism industry in post-crisis conditions.

Lee and Kong (2023) analyze the impact of COVID-19 and vaccination on global travel sentiment using a hybrid grey forecasting model enhanced with a residual modification approach to improve accuracy. Their findings reveal opposing effects of COVID-19 and vaccination on travel sentiment, emphasizing the need for governments to focus on pandemic control and vaccination to restore confidence and support tourism recovery. Yoga Laksito and Yudiarta (2021) highlight the critical role of effective planning in Bali's tourism sector, which is highly dependent on foreign visitors. Using the Even Grey Forecasting Model, they forecast tourist numbers and calculated financial losses for Bali during the COVID-19 outbreak in 2020, estimating a total of over $7.3 billion. Their study underscores the severe impact on the tourism economy and provides actionable insights for policymakers and businesses to aid recovery efforts. Sun et al. (2016) address the importance of accurate forecasting in China's international tourism industry, especially in response to economic disruptions like the 2008 financial crisis. They propose an optimized Markov-chain grey model to better manage market volatility and improve forecasting accuracy. The results demonstrate that this approach provides more efficient and precise forecasts for annual foreign tourist arrivals, supporting improved planning and decision-making by tourism agencies.

Grey forecasting models and univariate models have demonstrated remarkable effectiveness in tourism forecasting, especially during periods of disruption such as economic recessions, natural disasters and health crises like COVID-19. These approaches are particularly well-suited for managing uncertain, incomplete, and limited data conditions, which are often prevalent in post-crisis scenarios and developing countries. Grey models provide reliable forecasts that aid in impact assessment, recovery planning and policy development. Univariate models offer simplicity and efficiency by analyzing historical patterns within a single variable. Combined, these models serve as indispensable tools for building resilience and enabling informed decision-making in environments where comprehensive data and advanced computational resources are limited.

Four phases have been proposed as a research methodology for forecasting in inbound tourism. As depicted in Figure 1. The first phase involves data collection from reliable and international sources. In the second phase, after thorough checking and comparison, the forecasting model is selected. The third phase encompasses the application of the models with the collected data, producing the expected forecasting results. Finally, in the fourth phase, the models are evaluated using appropriate scales. Detailed explanations of each phase are provided Figure 1.

To conduct this research, it is essential to identify and secure the necessary resources while ensuring the accuracy and dependability of the data through the application of appropriate standards, procedures and tools (Thomas, 2021).

Data is extracted from official websites, published reports and tourism databases using either automated tools or manual extraction methods to guarantee accuracy and completeness. Primary sources consist of international tourism databases managed by organizations like the United Nations World Tourism Organization (UNWTO) and the World Travel and Tourism Council (WTTC), which provide global tourism data and trends. Secondary data sources include the Iranian National Tourism Organization, which offers comprehensive and reliable statistics on tourism. Additional data may be obtained from the Statistical Center of Iran, the Ministry of Cultural Heritage, Tourism, and Handicrafts, and other relevant governmental bodies.

Given the high validity of the official data provided by the UNWTO, this research utilizes data extracted from the UNWTO. The Tourism Dashboard of the UNWTO offers statistics and insights on key indicators of inbound tourism at both global and regional level (UNWTO, 2023). The data collected from the UNWTO dashboard is presented in Table 1. The dataset consists of annual records of inbound tourist arrivals from 2020 to 2023. A preliminary analysis revealed a gradual recovery in tourist numbers post-COVID-19, reflecting the easing of travel restrictions and the global recovery of the tourism sector. Given the annual nature of the data, forecasts are also made on an annual basis to ensure consistency and relevance to trend analysis.

In this study, data preprocessing was conducted to ensure the integrity and quality of the dataset used for forecasting. The dataset was checked for missing values, and it was confirmed to be complete, with no entries missing in the historical data. To assess potential outliers, we applied a standard deviation-based method, where values beyond three standard deviations from the mean were considered outliers. The calculated range for nonoutlier data was [−2713.96,8928.46], and all observed values fell within this interval. Thus, no significant outliers were detected in the dataset. Given that the data was already in the “Thousands” scale, no further normalization was required. This scale was directly applicable to the grey forecasting models, facilitating easy and consistent calculations.

Demand forecasting models can be classified according to factors like the type of forecast data and the number of variables taken into account, the nature of the problem and the specific industry for which the forecast is conducted, and the models used for forecasting. There are several quantitative techniques, but none of these models give good results with small and valid data and uncertainty conditions. Table 2 shows the historical data requirements of different models.

Grey forecasting models offer a distinct advantage in situations marked by data scarcity and uncertainty. Unlike traditional models that require extensive, stable datasets or involve complex computations, grey models can generate reliable forecasts from limited, inconsistent data. This makes them especially relevant in the post-COVID-19 era, where tourism and socioeconomic indicators have become volatile and unreliable. In such conditions, models that do not depend on stable explanatory variables are more effective. Grey models balance simplicity with predictive power, allowing meaningful insights to be drawn from minimal input. Their accessibility also empowers policymakers and stakeholders regardless of technical expertise to make informed decisions, positioning grey models as practical tools aligned with futures thinking in uncertain environments.

In control theory, color represents the clarity of available information. Control theory classifies systems based on data accessibility: white for complete information, black for none and grey for partial availability. Grey system focuses on analyzing uncertain systems with limited data, using known information to derive accurate insights and understand real-world dynamics. The core idea of grey systems is the presence of incomplete information (Karimi and Ahmadian, 2024).

In traditional statistical forecast models, a significant amount of data is necessary to fulfill the scale requirement. However, this condition cannot always be fulfilled. Therefore, new models that can be distinguished from traditional statistical models should be developed. The key characteristic of the grey forecasting approach is its ability to extract valuable information from the limited data available (Karimi et al., 2024). The grey forecasting model GM (1,1) model is based on the accumulated generating operation (AGO), a fundamental aspect of grey theory. The main purpose of AGO is to smooth the data by reducing its randomness and transforming it into a monotonic increasing function. In grey theory, differential whitening equations and time response functions are the primary tools used (Ahmadian, 2025).

Let $X$ represent a system behavior data sequence, and when the operator $d$ is applied to $X$⁠, the resulting data sequence $xd$ is provided in Eq.1.

Hence, $d$ is referred to as a sequence operator, and $xd$ is known as a first-order operator sequence. Each data $x(k)(k=1,2,...,n)$ of system behavior data sequence $X$ must be fully used in the whole process of the operator sequence. Applying an infinite buffer operator allows the transformation of the raw data sequence into a constant sequence. The discrete grey forecasting model, an advanced version of the traditional grey forecasting model, leverages the buffer operator to improve simulation accuracy (Ahmadian, 2025).

Grey differential model, denoted as $GM(1,1)$⁠, operates as a first-order model with a single variable, assessing and forecasting the values of studied indicators independently. The process includes applying an accumulating generation operator (AGO) to the data, solving the model's differential equation to determine the forecast value, and then using the inverse accumulating generation operator (IAGO) to obtain the forecast value for the original data. The following equations are the steps of $GM(1,1)$ (Ahmadian, 2025):

$a$ is the coefficient and $b$ is the grey control coefficient, $t$ is the independent variable. Eq.2 is the white differential equation of grey model $GM(1,1)$⁠.

Eq.3 represents the initial time sequence.

Eq.4 and Eq.5 represent the first-order accumulated generating operation (1-AGO).

Where $x(1)$ represents the accumulated data.

1-AGO matrix $B$ in Eq.6.

By applying the least mean square method, $a$ and $b$ is estimated in Eq.7 and Eq.8.

Where $BT$ represents the transpose of matrix $B$⁠, and $x(0)$ represents initial time sequence.

Using the estimated coefficients $a$ and $b$⁠, the grey forecasting equation can be formulated as shown in Eq.9, which provides the accumulated value at time $t+1$

Where $xˆ(1)$ represents forecasted accumulated value, and $t$ represents time counter.

By applying the inverse accumulated generating operation, Eq.10 and Eq.11 are obtained.

Where $xˆ(1)$ represents forecasted accumulated value, and $xˆ(0)$ represents forecasted initial value and $t$ represents time counter.

In Iran, the complexity and rapid changes in tourism systems during the COVID-19 pandemic create significant forecasting challenges. Grey forecasting models are ideal for these conditions, as they manage uncertainty and incomplete data effectively. This study selects and justifies the appropriate grey forecasting models to forecast inbound foreign tourists to Iran, ensuring accurate and reliable forecasts. Table 3 lists the chosen grey forecasting models and their specific justifications.

After collecting data and choosing the forecasting models, it will be time to implement the models. Python programming language was used to implement the model. In the model implementation, section, four grey forecasting models are used to forecast the number of inbound tourists to Iran for the years 2024–2026, based on data from 2020 to 2023. Each model is implemented with specific parameters tailored to the dataset. Results from each model are presented in a Table 4, detailing the forecasted tourist numbers for each year.

A visual comparison between forecasted values is provided in Figure 2 for better illustration of the differences among the models.

In the model evaluation stage, the forecast accuracy of each grey forecasting model is rigorously assessed using various error metrics (Ahmadian, 2025), such as Mean Absolute Error (MAE), Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE). By comparing the performance of the GM (1,1), RGM (1,1), Unbiased GM (1,1), Modified unbiased GM (1,1), DGM (1,1) and grey Verhulst models, the most suitable model for forecasting inbound tourist arrivals to Iran is determined. The evaluation results provided in Table 5 offer valuable insights into the strengths and limitations of each model, informing future research and decision-making in the tourism sector.

MAE measures the difference between the actual and estimated values and is expressed by Eq. 12 (Karunasingha, 2022).

RMSE is used as a standard for evaluating forecasting precision. It represents the standard deviation of the differences between the actual and estimated values. The RMSE is defined by Eq. 13 (Karunasingha, 2022).

MAPE is used to compare actual sequence and estimated sequence. MAPE are defined as Eq. 14 (de Myttenaere et al., 2016).

Where $x(0)$ represents original initial value, and $xˆ(0)$ represents forecasted initial value and $k$ represents time counter.

It is important to note that most forecasting do not perfectly align with reality, and efforts should be made to minimize forecast error. To compare model precision, three common evaluation tools are used.

Table 4 shows a significant increase in the actual number of inbound tourists to Iran from 2020 to 2023. The number of tourists rose from 1549600 in 2020 to 5780000 in 2023, representing a 274.54% increase. Forecasts for 2024 to 2026 suggest that this growth trend will continue, with all models forecasting that the number of inbound tourists will increase. In 2024, 2025 and 2026 the DGM (1,1) model forecasted significantly higher values compared to the other models, indicating a potential overestimation of future tourist numbers, and Grey Verhulst model lowest values compared to the other models. However, the Grey Verhulst model forecasted lower values for 2025 and 2026, suggesting a more conservative estimate. It is important to note that these forecasts are based solely on historical data, and various factors such as global political and economic conditions, international events and natural disasters can also affect the number of inbound tourists to Iran.

During the model evaluation stage, the forecast accuracy of each grey forecasting model was rigorously assessed using various error metrics, such as MAE, RMSE, and MAPE. By comparing the performance of the GM (1,1), RGM (1,1), Unbiased GM (1,1), Modified Unbiased GM (1,1), DGM (1,1) and Grey Verhulst models, the most suitable model for forecasting inbound tourist arrivals to Iran was determined. The evaluation results provide valuable insights into the strengths and limitations of each model, informing future research and decision-making in the tourism sector. From the error metrics, it is evident that the Modified Unbiased GM (1,1) model exhibited the lowest MAPE at 23, indicating its superior accuracy in forecasting inbound tourist numbers. The GM (1,1) model also performed well with a relatively low MAE of 466 and RMSE of 588. On the other hand, the RGM (1,1) model had the highest error values in MAE and RMSE, reflecting its poor performance in this context. The DGM (1,1) model's high error metrics suggest that it may not be suitable for this particular dataset, potentially due to overfitting or sensitivity to the data's characteristics. The Grey Verhulst model, while more conservative in its forecasts, showed moderate performance with an MAE of 870 and RMSE of 1063, which is the second lowest of all the models, indicating its superior accuracy in forecasting the number of inbound tourists to Iran. RMSE for the GM (1,1) model is 588, also the first model among all the models; RMSE for the Grey Verhulst model is 1063, also the second model among all the models, highlighting its accuracy in forecasting the average error in the number of inbound tourists. MAPE for Modified unbiased GM (1,1) model is 23, the first lowest of all the models; MAPE for the Unbiased GM (1,1) model is 24, the second lowest of all the models, demonstrating its accuracy in forecasting the percentage error in the number of inbound tourists. Considering the measures of inaccuracy, the analysis indicates that for forecasting inbound tourist arrivals to Iran, the GM (1,1) and Grey Verhulst approaches demonstrate superior performance compared to alternatives.

This study makes a significant contribution to tourism forecasting, particularly in the post-pandemic recovery context, by evaluating grey forecasting models for forecasting inbound tourism to Iran. Grey models, particularly GM (1,1), have been found to be well-suited for handling small and volatile datasets, a characteristic common in post-pandemic tourism data. Univariate forecasting plays a vital role in tourism recovery due to its speed and simplicity, making it highly effective in data-scarce environments. Unlike complex multivariate models that require extensive data and computational resources, univariate models provide practical, quick insights, which are particularly beneficial for policymakers in developing countries.

A key advantage of grey forecasting models lies in their simplicity and accessibility. These models do not require advanced econometric knowledge or complex datasets, making them suitable for tourism professionals facing resource constraints, especially in the post-COVID-19 era, where reliable data may be limited. However, certain limitations are acknowledged in this study; the reliance on post-pandemic data (2020–2023) may not fully capture long-term trends or broader shifts in tourism patterns. While grey forecasting models are highly effective for short-term predictions, their long-term forecasting capabilities may be limited, particularly in the face of unpredictable external factors such as economic downturns or geopolitical instability. To enhance forecasting accuracy, incorporating socioeconomic and external variables such as economic growth rates, political stability and global crises into these models would provide a more comprehensive understanding of tourism trends during periods of disruption.

The findings align with broader tourism recovery trends, emphasizing the importance of forecasting models in shaping tourism strategies. These insights are essential for policymakers and industry stakeholders seeking to adapt to post-pandemic changes in travel behavior. Additionally, by comparing different grey models, the study offers insights into their performance and provides a methodological alternative for decision-making in uncertain environments, aligning with futures thinking principles. This study highlights how such approaches allow for efficient decision-making under uncertainty, reinforcing their situational relevance.

By applying advanced grey models, this research contributes to academic discourse on futures thinking and forecasting, offering a methodological alternative for tourism researchers and practitioners operating in data-constrained environments. Precise forecasting plays a vital role in adjusting to evolving tourism trends, particularly in the post-COVID-19 landscape, where travel patterns have significantly shifted. This study underscores the importance of future-oriented forecasting, illustrating how grey models contribute to adaptive and strategic planning in uncertain tourism markets. By utilizing these models, policymakers can obtain valuable insights that extend beyond immediate recovery, allowing them to anticipate emerging trends and proactively navigate changing industry conditions. The study compares six different grey forecasting models to predict inbound tourism to Iran for the years 2024–2026, based on post-pandemic data from 2020 to 2023. The results indicate that the Modified Unbiased GM (1,1) model provides the highest forecast accuracy. This study enhances the theoretical foundation of forecasting in uncertain environments by integrating established futures thinking frameworks and grey forecasting models. It underscores the role of forecasting models not only as short-term decision-making tools but also as essential instruments in uncertain conditions in tourism recovery. The findings highlight the effectiveness of grey forecasting models in handling small datasets, particularly in post-crisis contexts where data availability is scarce.

The findings of this study, particularly the generated forecasts, have significant practical implications for driving the post-pandemic tourism recovery in Iran. The forecasted surge in inbound tourists presents a valuable opportunity for policymakers and industry stakeholders to strategically plan and optimize resources. Policymakers can leverage these forecasts to develop and implement supportive policies such as facilitating visa processes, investing in infrastructure development and running targeted marketing campaigns to attract international visitors. Tourism authorities can utilize this data to allocate resources effectively, design impactful promotional strategies and prepare for increased demand in the hospitality and transportation sectors. The projected tourism growth will require a focus on enhancing service quality, diversifying product offerings and adopting dynamic pricing strategies in the hospitality industry to cater to the growing demand. Additionally, transportation policies should focus on improving public transit, road infrastructure and accessibility to tourist destinations to handle the increased traffic. Furthermore, the study underscores the importance of proactive planning and risk management to address potential challenges in the tourism sector. Stakeholders should develop contingency plans to address economic fluctuations or unforeseen global crises while continuously monitoring tourism trends and adapting strategies accordingly. In light of the findings, stakeholders should also invest in workforce training and technological advancements for service delivery. Embracing innovations in the tourism sector will be crucial for effectively managing the forecasted growth. Additionally, fostering collaboration across various sectors, such as tourism, infrastructure and hospitality, will help ensure that Iran capitalizes on the post-pandemic tourism boom. These practical implications will not only drive economic growth but also create employment opportunities and showcase Iran's rich cultural heritage to the global market. By implementing these strategies, Iran can optimize its tourism potential and improve its resilience against future uncertainties.

The reliance on a relatively short dataset (2020–2023) limits the ability to capture long-term tourism trends. Furthermore, while grey forecasting models are highly effective for short-term predictions, their capacity for long-term forecasting is limited, especially when external factors such as economic conditions or geopolitical events are unpredictable. Moreover, the exclusion of socioeconomic variables in the forecasting model is a notable limitation. Including factors such as economic growth, political stability, and changes in international relations would enhance the accuracy and relevance of the forecasts. However, it should be noted that grey forecasting models are particularly well-suited for scenarios where data on influencing variables is scarce or unreliable. In situations characterized by uncertainty or limited access to accurate data, these models offer a practical and effective approach to forecasting. Their ability to work with small, uncertain datasets makes them a valuable tool for forecasting in environments where other forecasting models may struggle due to the lack of complete or reliable data.

Future research should build upon this study's insights to refine forecasting approaches for tourism recovery. While this research provides valuable guidance for resource allocation, marketing strategies, and infrastructure planning, further studies could incorporate stakeholder feedback and sector-specific needs to enhance practical applications. Additionally, the exclusion of socioeconomic and external factors remains a limitation, as these variables significantly influence tourism trends, particularly during periods of disruption like the post-pandemic era. Future studies should integrate these elements to improve forecasting reliability and provide a more comprehensive understanding of tourism demand. Although the presented model, based on post-pandemic data (2020–2023), offers useful short-term forecasting, its focus on this limited timeframe restricts its ability to capture long-term shifts in travel patterns. A more robust forecasting approach would incorporate pre-pandemic data, recovery trends and emerging market conditions, enabling a broader perspective on evolving consumer behavior. Future research could develop models that combine these models for more accurate forecasting. Grey forecasting models have shown strong applicability in data-scarce environments, but integrating them with machine learning techniques could significantly enhance forecasting precision. Future research should continue exploring hybrid methodologies that merge grey forecasting with machine learning to enhance predictive accuracy. Hybrid models could improve adaptability in complex post-crisis scenarios where tourism data evolves unpredictably, contributing to the development of more resilient predictive frameworks for crisis management and recovery.

The author acknowledges that part of the methods section in this article overlaps with the methods used in the paper titled “E-payments in the post-COVID-19: navigating uncertainty and forecasting trends” (DOI: https://doi.org/10.1108/JES-11-2024-0745). The author also used AI tools to improve the clarity of language and grammar.