Air transportation under COVID-19 pandemic restrictions: A wavelet analysis

1. Introduction

Over recent decades, air transportation has become an essential stimulus for developing international trade in parallel with the intensification of worldwide mobility. Many other connected economic sectors have extended significantly, both vertically and horizontally, from aviation production to ground handling services (i.e. passenger service, cabin service, catering, ramp service, and field operation service).

Discovered in December 2019 around Wuhan, China, Coronavirus 2 (SARS-CoV-2) rapidly spread worldwide, unfortunately causing more than 2 million fatalities in January 2020. The official declaration of COVID-19 as a pandemic by the World Health Organization (WHO, 2020) on March 11th, 2020, generated a strong recoil in all socio-economic domains, irreversibly influencing people's lives. Sumner et al. (2020) stress that this disease caused the strongest global recession after the Great Depression from 1929 to 1939.

The aviation sector did not escape either. On the contrary, it was one of the most affected sectors. According to the Flightradar24 (2022) website, commercial flights dramatically dropped worldwide by over 80% in April 2020, compared with January of the same year.

The pandemic effects on the aviation industry are well-depicted by Sun et al. (2021). Many companies entirely suspended their operations or reduced them (Sun et al., 2020), while others preferred to fly empty aircraft in order not to lose their airport-attributed slots (Haanappel, 2020). To compensate for these losses, some companies alternatively transformed their passenger cabins into cargo storage space (Sun et al., 2021). Drastic limitations of flight ground conditions were also observed. Many airports severely restricted the number of slots or fully closed them (Adrienne et al., 2020), especially to obtain aircraft parking places. Ground handling services were significantly reduced and were covered by rotation with minimum staff (Iacus et al., 2020). Not least, aircraft producers reduced or shut down their lines of production (Truxal, 2020). Fortunately, as Sun et al. (2021) emphasise that the aviation industry seems to be resilient to different shocks, including from oil, financial, and economic crises to wars and global diseases.

At the same time, the aviation industry was accused of playing an important role in the spread of different diseases in history (Sun et al., 2021), with many epidemics becoming pandemics (e.g. Ebola - Pigott et al., 2014; SARS/MERS - Wong et al., 2015; seasonal influenza - Khan et al., 2009; Malaria or Dengue fever - Tatem et al., 2006).

In light of the recent pandemic disease, the area managed by the European Organisation for the Safety of Air Navigation (Eurocontrol)1 deserves special interest, with this zone registering one of the highest air traffic densities in the world (Figure A1, Appendix). Herein, the COVID-19 pandemic expressed as new cases and total flights exhibited interesting dynamics in the last two years, requiring additional investigations, as Fig. 1 illustrates.

Fig. 1.

New COVID-19 cases and total flights in the Eurocontrol zone over 01/03/2020 - 31/12/2021.

Sources: performed based on datasets freely offered by the Our World and Data, 2022a, Our World and Data, 2022b, Our World and Data, 2022c, Our World and Data, 2022d, and Eurocontrol (2022).

Fig. 1 shows various sub-periods in dynamic terms at the Eurocontrol level, with the same or opposite signs between new COVID-19 cases and total flights. The collapse of commercial flights is clearly evidenced in April 2020. Further, the evolutions are generally the same, with exceptions related to summer vacations (i.e. August–September 2020, and June–September 2021) and visible progress of vaccination plans despite the explosion of new cases starting in October 2021.

According to Eurocontrol (2021), all-cargo flights represent 3 or 4% of total European flights in normal years. However, they made up more than 25% of total European flights at the beginning of July 2020, after the lockdown from April 2020 caused by the COVID-19 crisis. At the end of January 2021, all-cargo flights maintained a market share of 10–11%, which is 3 or 4 times the normal share (Eurocontrol, 2021). Restricted to the official dataset availability, Fig. 2 plots the dynamic of flights at the Eurocontrol zone, as they are passenger, cargo (i.e. freight and mail) and other types of flights.

Fig. 2.

Total, passenger, cargo and other types of flights in the Eurocontrol zone over 01/03/2020 - 06/02/2021.

Sources: performed based on datasets freely offered by Eurocontrol (2022).

Note: left scale - total and passenger flights; right scale - cargo and other flights.

The figure points out the collapse of passenger flights from April 2020 because of the COVID-19 shock, with passenger flights representing more than 90% of total European flights at that time (Eurocontrol, 2021). Further, a notable recovery of passenger flights is registered starting with May 2020. In parallel, a smoothly ascending trend is observed for cargo flights, especially due to special needs occasioned by the pandemic context. Finally, the other types of flights show a similar increasing trend, with a peak in May 2020, many of them related to repatriation, medical or other special necessities.

Therefore, the sign and intensity of connection between the new COVID-19 cases and total flights require additional investigations regarding their lead-lag status by also considering any potential asymmetry determined by the flight typologies.

The paper analyses the interaction between the pandemic progress and air transportation in this context by assuming a two-way co-movement. The empirical part is supported by wavelet methodology, over the period from 01/03/2020 - 31/12/2021, at the Eurocontrol area. The connection is controlled through COVID-19 tests, COVID-19 vaccinations, other policy responses, oil prices, financial stress conditions and a measure of aviation industry performance.

The main results show a strong link between the pandemic and air transportation in the very short- and short-terms. The direction of co-movement running from pandemic to air transportation or from air transportation to pandemic mainly depends on pandemic dynamics and policy responses, especially related to testing and vaccination. These results are robust with respect to passenger flights but sensitive to cargo and other types of flights. In the medium-term, the lockdown and pandemic maxima are the key ingredient for ‘pandemic - air transportation’ nexus as well as the typology of flights. Those interactions better characterise the hub-countries, with high air traffic and extended disease spread. Financial stress, oil prices and performance in the air sector are relevant 'binders' of link in the medium-term.

Pandemic spread limits flights due to officially imposed restrictions following the pandemic signal (i.e. social distancing, lockdowns, mask mandates, testing, or vaccination), induces a fall in demand determined by general concern, and/or reduces the production of aviation industry because of lockdown. Therefore, the overall collapse of flights is not explained only by the physical spread of pandemic disease but also by its psycho-behavioural consequences.

Conversely, air transportation involves human activities implying passengers and employees who are directly or indirectly involved in this sector (i.e. ground, in-flight or adjacent sectors). Therefore, air transportation influences pandemic spread through social distance by airport size and its connection facilities, internal screening procedures, boarding methods and/or in-flight rules. In other words, the pandemic spread is affected by ground, in-flight or adjacent specific air transportation activities, including all types of related passengers and employees.

The contribution of the paper is fivefold. First, to the best of our knowledge, the study is one of the first contributions exploring the relationship between pandemic and air transportation at the Eurocontrol level in a two-way vision (i.e. pandemic to air transportation and vice versa). This is very important for policy responses as such an approach allows for drawing policy adjustments relying on an inter-conditional context. In other words, the policy concomitantly considers not only the effects running from the pandemic or air traffic but also their interactional implications. Second, unlike the existing studies, a much-extended set of determinants is integrated to find more insights regarding the ‘COVID-19 pandemic - air transportation’ nexus, such as the tests, vaccinations, pandemic policy responses, oil prices, financial stress conditions and performance of the aviation industry. Third, also as a novelty in the field, the sensitivity of the link is tested by considering the typology of flights (i.e. passenger, cargo and other categories) and country-hub characteristics in order to capture any induced asymmetry in the relationship. Fourth, the study supports the consideration of a new methodology in the field by wavelet type. Only the paper of Fareed et al. (2022) globally explores the interaction between the COVID-19 pandemic and air transportation by using wavelet methodologies (i.e. continuous wavelet transformation and wavelet coherence) over the period from January 2020 to September 2020. Unlike this, our study explores a more extended period (i.e. January 2020–December 2021) by mixing additional wavelet methods, ranging from wavelet coherency to multiple and partial wavelet coherence. Compared with time-series approaches, wavelets offer superior results by identifying “deep details about the intensity of co-movement between variables over time and frequencies by following their lead-lag status on short-, medium- and long-runs” (Mutascu and Sokic, 2021, p. 208). Therefore, the classical time-domain methods do not allow obtaining details on sub-periods of time, their results strictly regarding the whole sample. As socio-economic processes vary over time, the results obtained based on conventional time-domain tools are practically inconsistent, potentially leading to wrong conclusions. Finally, it is noteworthy that this study follows a non-linear analysis by testing variables' ‘lead-lag’ status over different sub-periods of time across frequency bands. According to Jordanov and Nikolova (2013), biological, natural and social processes generally have nonlinear dynamics. Therefore, air transportation activities dominated by human behaviour are less likely to follow a pure linear tendency. Unfortunately, many existing papers in the field widely consider linear assumptions by empirically employing classical time-domain econometric methodologies.

The rest of the paper is organised as follows: Section 2 reviews the literature, Section 3 presents the data and methodology, Section 4 shows the main results, and Section 5 performs the robustness checks. Finally, Section 6 concludes.

2. Literature review

There is a vast literature regarding the relationship between the COVID-19 pandemic and air transportation. Sun et al. (2021) offer a useful and extended review. They focus on the interaction between COVID-19 disease and the aviation sector, also considering aviation as potential means of virus spread. The literature covers 110 papers from the year 2020, with different targeted countries, methodologies and datasets, providing heterogeneous results. Both quantitative and qualitative studies are conducted. More recently, Sun et al. (2022) extend their previous study by adding nearly 200 papers from 2021 to 2022. Herein, the contributions are grouped into eight categories: airlines, airports, passengers, workforce, markets, contagion, sustainability, and economics.

Inspired by Sun et al. (2021) and Sun et al. (2022), three strands of literature are identified regarding the relationship between the COVID-19 pandemic and air transportation. The first strand is devoted to the impact of the COVID-19 pandemic on air transportation. The second strand is focused on the implications of air transportation on the COVID-19 pandemic, while the third strand considers the two-way relationship between air transportation and the COVID-19 pandemic.

2.1. Influence of the COVID-19 pandemic on air transportation

The first strand of literature explores the influence of the COVID-19 pandemic on air transportation through flight suspensions, reductions in demand, and financial issues in the aviation industry.

One of the first impacts of the pandemic's official declaration (March 2020) was the wide suspension of commercial flights between March and May 2020. Pioneering work in the field belongs to Albers and Rundshagen (2020), who analyse the reactions of flight operators to pandemic shocks by reviewing the information from the newsletter ‘Aviation Week Network’. They find a set of reactions, ranging from retrenchment and innovation to exit and resumption. Similarly, Budd et al. (2020) state that many companies changed their flight operations and reconfigured their capacities in parallel with rationalisation measures and staff reductions. Li et al. (2020) compares the reaction of the Chinese air cargo sector with the passenger sector, concluding that the cargo sector was less negatively affected than the passenger one. Further, Nižetić (2020) obtains the same conclusion but for the flights in the European Union (EU) case. Unlike them, Da Silveira Pereira and Soares de Mello (2021) show that air companies with a better mix of aircraft models had a more efficient response to the COVID-19 outbreak despite the registered rebound. A negative impact of the COVID-19 pandemic on air transportation is also evidenced by Sun et al. (2020) but following a different level of fractality.

In the same vein, Sun et al. (2021a) treat an extended set of countries, over January 05/01/2020 - 15/05/2020, with data collected from www.flightradar24.com. They analyse the degree of synchronisation between the numbers of confirmed cases in parallel with how/at which stage those countries adapted their air transportation operations. The authors underline that in the majority of the countries, the borders were unfortunately closed too late. The same authors explore three COVID-19 variants to see how the existing flights were restricted due to concerns regarding those newly emerged virus forms (Sun et al., 2021b). A classical compartmental Susceptible–Exposed–Infectious–Recovered (SEIR) model supports the main findings by considering the Alpha, Beta and Gamma variants for the years 2020 and 2021. The authors show that many countries banned flights too late; the mutated virus had sufficient time to spread worldwide through air transportation.

The air traffic disruption and temporary suspension are also indirectly explained via the psycho-behavioural experience of crewmembers. More precisely, the pandemic generates stress (Sechko, 2021), depression (Cahill et al., 2021), fatigue (Drogoul and Cabon, 2021), and burnout (Ozturk, 2020), accompanied by a reduction of flight performances, as Sun et al. (2022) note.

Other researchers focus on the collapse of air transportation demand as a reaction to COVID-19, with almost all papers suggesting a negative impact. For example, Abate et al. (2020) argue that the fall in demand is relevant for the tourism and business segments, with the reduction expected by the end of 2021. Gallego and Font (2021) demonstrate a linear decrease of air transportation demand, while Gudmundsson et al. (2020) claim a general recovery period of around 2.4 years, with 2.2 years for passenger demand. In the same context, Lamb et al. (2020) conduct a survey with 632 passengers and show that the main worry when flying comes from the perceived threat of COVID-19. Similarly, Andreana et al. (2021) highlight the negative impact of the COVID-19 outbreak on air transport, its magnitude being higher than any previous crises. The authors explain this demand compression by reduction of passengers’ propensity to travel due to pandemic concerns, with long-term persistence. Moreover, DeLaura et al. (2021) claim that the classical factors influencing air transportation demand, such as price and service quality, became of secondary importance during the pandemic disease. In the same vein, Li et al. (2021) analyse the effects of pandemic disease on the spatiotemporal variation of the worldwide air transportation network (WATN). They evidence a dynamic pattern of decline and recovery in 2020 for the performance of the WANT. Likewise, Li et al. (2022) investigate the impact of the COVID-19 pandemic on air transportation but focus on China. Their between-within estimations over April 20, 2020–April 30, 2020 reveal that the restoration of the aviation industry and other connected industries is the result of control measures adopted during the early stage of the pandemic.

Several papers treat the financial impact of the COVID-19 pandemic on air transportation. For example, Nhamo et al. (2020) assess the financial status of airports, observing a substantial decline in revenues. Many airports ceased almost all operations, being forced to convert into air parking places. Agrawal (2021) identifies the cash reserves and solvency of Indian airlines as two of the most altered financial indicators under the COVID-19 shock. Unlike them, Chen et al. (2020a) study the United States (US) air sector in parallel with travel and leisure companies, pointing out that returns in the air sector were the most negatively affected. Differently, Truxal (2020) reveals that not only the airlines were financially negatively affected but also the aircraft producers, with many manufacturers reducing/shut-downing their production (Truxal, 2020).

Kim and Sohn (2022), who examine the US airline market reaction to exit decisions using a logit methodology, offer a more complex analysis. They show that before and after a pandemic, shocks are crucial for exit decision but varies across the markets, airports and airlines. Interestingly, larger hub airports are more likely to be exited than non-hub airports after a pandemic.

2.2. Impact of air transportation on the COVID-19 pandemic

The second strand of literature focuses on the impact of air transportation on the COVID-19 pandemic via a few key elements, such as connection facilities, screening procedures, boarding methods and/or in-flight rules.

Generous literature is devoted to the role played by connection facilities as a driver of COVID-19. As Sun et al. (2021) note, connectivity and short travel time are beneficial for passengers but harmful in the pandemic context. One of the first contributions belongs to Coelho et al. (2020), who stress that the exponential growth rate of a pandemic is caused by population and the number of airport connections. For example, Daon et al. (2020) claim that airports from East Asia are more prone to spread the disease compared with those from India, Brazil, or Africa. Lau et al. (2020) find a positive correlation between the volume of domestic and international passengers and the spread of COVID-19. They examine China by using linear regression models. More nuanced are the conclusions of Li et al. (2020), who show that the flight spread effect can be controlled, but only in the short term. As a novelty, Nakamura and Managi (2020) propose the concepts of ‘exportation’ and ‘importation’ of disease from one airport to another, proposing a reduction of mobility to control the magnitude of the spread. In this vein, Tuite et al. (2020) confirm their ideas by investigating the flight connections between Iran and other countries. In a recent paper, Choi et al. (2022) investigate how air travel mobility and global connectivity widely spread the COVID-19 virus in its major variants (i.e. Alpha, Beta, Gamma, and Delta). Using regressions, they emphasise that air network connectivity is a prominent means of the virus spreading, while healthcare infrastructure plays a minor role in the timely prediction and detection of the virus.

Various findings are observed when screening procedures are targeted. Hence, the screening procedures are shown to be ineffective in reducing the export of COVID-19 by Dollard et al. (2020), because of nonspecific clinical characteristics or asymptomatic cases. Mitra et al. (2020) obtain similar conclusions, while opposite ones are revealed by Normile (2020), and Serrano and Kazda (2020), who highlight the crucial role of temperature screening despite its expensive costs. In the same screening framework, De Neufville and Neufville (1995) underline the importance of airport status as it is involved in the local competition (catchment area) or global competition (as a transfer hub).

The choice of boarding method is also analysed as a pandemic spread possibility. For example, Cotfas et al. (2020) argue that less infection is observed in the case of back-to-front by row boarding. Contrary, Islam et al. (2021) sustain that the back-to-front method doubles passengers’ exposure. They recommend random boarding, which is reinforced by Schultz and Fuchte (2020).

Finally, several papers are devoted to the in-flight rules and their implications for COVID-19 spread. For example, Bielecki et al. (2021) show that the probability of being infected during in-flight travel is about 1 per 27 million, assuming that all required safety protocols are followed. Chen et al. (2020b) compare the pre-flight with in-flight contexts, emphasising that the virus transmission rate is generally higher during pre-flight exposure. Otherwise, Schwartz et al. (2020) defend the in-flight lack of infection. They analyse a flight between Guangzhou and Toronto and find that cases of in-flight transmission are rare.

2.3. Two-way relationship between air transportation and the COVID-19 pandemic

The last strand of literature is devoted to the bi-directional link between air transportation and COVID-19. Only one paper seems to analyse the relationship between the COVID-19 pandemic and international air traffic in a two-way approach by using wavelet methodology. More precisely, Fareed et al. (2022) employ the continuous wavelet transform and wavelet coherence methods in a global study over the period from January 2020 to September 2020. Observing the co-movement between only two variables, the authors find evidence of intensive interaction between COVID-19 and international air travel from January 2020 to September 2020, at 32–64 days band of scale. Herein, COVID-19 negatively drives international air travel. Additionally, they claim that international flights spread the COVID-19 virus worldwide from May 2020 to mid-June 2020, at 4–8 days band of scale. According to Fareed et al. (2022), their results are in line with those of Yang et al. (2020) and Zhang et al. (2020). For example, Yang et al. (2020) find that COVID-19 is transmitted in aeroplanes but with mild symptoms, while Zhang et al. (2020) conclude that the number of COVID-19 cases in the destination Chinese cities is positively correlated with air flights and high-speed train services out of Wuhan.

In summary, the literature shows evidence of a two-way co-movement between the COVID-19 pandemic and air transportation. Generally, the COVID-19 pandemic negatively influences air transportation, while air transportation reveals a conclusive sign regarding the COVID-19 disease spread.

Several main literature gaps are identified. First, a scarcity of papers that simultaneously explore both directions of co-movement between the COVID-19 outbreak and air transportation is observed, at the Eurocontrol level, in a nonlinear fashion. Out of them, only Fareed et al. (2022) are found treating the link from time-frequency domain perspectives, but singularly considering wavelet coherence tool at the global level. Almost all contributions consider a linear connection supported by classical time-series regressions. Second, no study controls for the link via different pandemic and socio-economic determinants by offering information on sub-periods of time. The major part of the contributions use such factors attaching the results to the entire investigated period. Finally, no paper treats the lasting effect of the ‘COVID-19 pandemic - air transportation’ nexus at different sub-periods of time by controlling for the nexus with different determinants inspired by literature. Therefore, this paper addresses all of these gaps.

3. Dataset and methodology

3.1. Dataset

The bivariate nexus between the COVID-19 pandemic and air transportation represents the core of the analysis. The sample has a daily frequency covering the period from 01/03/2020 to 31/12/2021 at the Eurocontrol level. The period is chosen to capture precisely the official beginning of the pandemic (March 2020), the acceleration of COVID-19 testing (after April 2020) and the beginning of the vaccination campaign (December 2020).

Pandemic (Pandemic) is captured through the number of new COVID-19 cases per million persons. The variable allows for the measurement of the volume of newly infected persons and the magnitude of disease spread in a given statistical population. This measure should be treated as a pandemic signal rather than a quantification of pandemic magnitude per se. The content of this variable covers a de facto dimension (i.e. spread of disease as magnitude) and a psycho-behavioural component (i.e. signal shaping human behaviour). The data are taken from Our World in Data online database.

Air transportation (AT) variable denotes the intensity of air traffic captured via total daily flights. Total flights include commercial passenger flights, cargo flights, charter flights, business jet flights, and other flights (i.e. private flights, gliders, most helicopter flights, most ambulance flights, government flights, some military flights, and drones). It is noteworthy that the measure comprehensively captures the magnitude of all air transportation activities by considering both passenger and non-passenger traffic (Fareed et al., 2022). The dataset is freely available in Eurocontrol online database. In parallel, a sub-set of air transportation variables is considered for testing the asymmetry of interaction between the pandemic and typology of flights, such as passenger (ATP), cargo (ATC) and other types (ATO) of flights, all expressed in daily flights. The sub-set is taken from Eurocontrol online database but is limited to a shorter period due to its official restrictive availability (i.e. 01/03/2020 - 06/02/2021).

For robustness checks, six other variables are considered to control the ‘pandemic - air transportation’ nexus: tests, vaccinations, policy response, oil prices, financial stress conditions and performance of the aviation industry.

The number of COVID-19 tests (Tests) and COVID-19 vaccinations (Vaccinations) reflect the magnitude of newly tested persons per million and the number of newly vaccinated persons per thousand, respectively. Both variables are obtained from Our World in Data online database.

COVID-19 policy response (CPR) is captured via COVID-19 Containment and Health Index as a composite index covering policy response in terms of school closures, workplace closures, travel bans, testing policy, contact tracing, face coverings, and vaccine policy rules. The index ranges from 0 (no policy) to 100 (strictest policy) as an aggregated daily average for the whole Eurocontrol zone. Despite heterogeneity in policy responses across Eurocontrol countries, we assume a strong cross-country dependence because any policy shock in a country can be easily transmitted to another as changing interacted magnitude in air traffic. The source of this dataset is Our World in Data online database.

The financial stress (OFR) variable represents the Financial Stress Index. The dataset is freely available in the Office of Financial Research database. Oil price (Brent) is captured via the Europe Brent Spot Price FOB, expressed in Dollars per Barrel. The dataset is taken from the Energy Information Administration of the United States online database.

Finally, the performance of aviation industry ( STOXX ) is measured via the STOXX Europe Total Market Aerospace & Defense (STOXX), expressed as a volume in Euros. The dataset is taken from Qontigo online databases.

The variables are expressed in their natural logarithm forms. Initially, AT, ATP, ATC, ATO, Pandemic, Tests, Vaccinations and OFR variables have been upwardly rescaled to obtain strict positive values when taking natural logarithms, not affecting their statistical distribution (i.e. each value has been increased by 1 in the case of AT, ATP, ATC, ATO, Pandemic, Tests and Vaccinations, and by 5 in the case of OFR).

For all estimations, the variables are considered in their level as the stationarity condition is not required propriety in the time-frequency approach (Aguiar-Conraria et al., 2008). White noise is also analysed to avoid bias in estimations (Mutascu, 2018).

3.2. Methodology

The interaction between the COVID-19 pandemic and air transportation is analysed empirically using the wavelet method. Wavelet is an oscillation by a waveform that starts at the beginning with zero amplitude, increases and decreases, and finally returns to its zero level. Often called a “brief oscillation”, the wavelet is generally a repetitive process over time and provides a kind of specific “lens” enabling a deep exploration of a time series. The core idea of wavelet methodology is to decompose a time-series into two components: one in time and another in frequency. The Morlet wavelet function ψ ₀ (η) by time η and frequency ω₀ is called to facilitate this process, having this shape:

$${\psi }_0\left(\eta \right)={\pi }^{-\frac{1}{4}}{e}^{i{\omega }_0\eta }{e}^{-\frac{1}{2}{\eta }^2}\text{,}$$ (1)

where i denotes $\sqrt{-1}$, while frequency is set to 6 in order to fit the admissibility condition proposed by Farge (1992). Unlike many other types of wavelet functions, Morlet offers better results because of “a good balance between time and frequency localization” (Grinsted et al., 2004, p. 563). The frequency is related to the wavelet's oscillation by sinusoidal form, with angular frequency ω₀ in an interval of a specified length centred at a moment t. Therefore, the wavelet is compressed and decompressed over time and across different frequencies, often called bands of scale.

Decomposition follows the continuous wavelet transformation (CWT) contrasting with discrete wavelet transformation (DWT). DWT is generally used for series treatment, while CWT is more appropriate for feature-extraction purposes (Tiwari et al., 2013; Mutascu and Sokic, 2021), showing “how the cross-wavelet analysis could be fruitfully used to uncover time-frequency interactions between two economic time-series” (Aguiar-Conraria and Soares, 2011, p. 647). Therefore, CWT is more appropriate for this analysis, as its main goal is to obtain detailed time-frequency (scale). CWT is characterised by a high measure of redundancy (i.e. significant overlap between wavelets at each scale and between scales) that allows for generating an accurate time-frequency spectrum. As Addison (2018, p. 1) emphasises, “in the context of the CWT, ‘redundant’ is not a pejorative term, it simply refers to a less compact form used to represent the information within the signal. The benefit of this new form - the CWT - is that it allows for intricate structural characteristics of the signal information to be made manifest within the transform space, where it can be more amenable to study: resolution over redundancy.”

Concretely, in the case of a discrete time-series {x _n }, with n=0 … N-1, the CWT has this form:

$$w_n^x\left(s\right)=\frac{\delta t}{\sqrt{s}}\sum _{n^{\prime }=0}^{N-1}{x}_{n^{\prime }}{\psi }^{*}\left(\left(n^{\prime }-m\right)\frac{\delta t}{s}\right)\text{,}$$ (2)

where, δt represents the time spacing at scale s, with m=0, 1, …, N-1. The scale is a concept related to the dilation or scaling wavelet process as the distance between the beginning and the end of a wavelet oscillation, the scale value being a fractional power of 2 (Rösch and Schmidbauer, 2018). More precisely, the wavelet function compresses under a small scale capturing high frequencies and decompresses under a long one capturing low frequencies.

Further, the wavelet coherency (WTC) allows analysing the intensity of interaction between two series {x _n } and {y _n }, having this formula:

$$R_n\left(s\right)=\frac{\left|S\left(s^{-1}{W}_n^{xy}\left(s\right)\right)\right|}{S{\left(s^{-1}\left|W_n^x\right|\right)}^{\frac{1}{2}}S{\left(s^{-1}\left|W_n^y\right|\right)}^{\frac{1}{2}}}$$ (3)

where S illustrates the smoothing operator in both time and scale, while $W_n^x$ and $W_n^y$ are the wavelet transforms of x and y.

WTC shows “the ratio of the cross-spectrum to the product of the spectrum of each series, and can be thought of as the local correlation, both in time and frequency, between two time series” (Aguiar-Conraria et al., 2008, p. 2872) note.

Finally, the phase difference is also performed. The method allows us to see the sign of the link between $W_n^x$ and $W_n^y$, and their related lead-lag status. The mean and confidence interval of phase difference depicts the phase difference φ _x,y (Aguiar-Conraria et al., 2008), with this form:

$${\phi }_{x,y}={\mathit{tan}}^{-1}\left(\frac{\mathfrak{I}\left\{W_n^{xy}\right\}}{\mathfrak{R}\left\{W_n^{xy}\right\}}\right)\mathrm{a}\mathrm{n}\mathrm{d}{\phi }_{x,y}\in \left[-\pi ,\pi \right]\text{,}$$ (4)

where ℜ is the real part of a complex number, while ℑ denotes the imaginary one.

Four cases can be identified. The time series move together over frequency when the phase difference is zero (i.e. series are in phase). Herein, x leads y when ${\phi }_{x,y}\in \left[0,\frac{\pi }{2}\right]$, and y leads x for ${\phi }_{x,y}\in$ $\left[-\frac{\pi }{2},0\right]$. Otherwise, the time series move opposite one another over frequency when the phase difference is π or –π (i.e. series are in anti-phase). In this case, x leads y when ${\phi }_{x,y}\in \left[-\pi ,-\frac{\pi }{2}\right]$, while y leads x for ${\phi }_{x,y}\in \left[\frac{\pi }{2},\pi \right]$.

All estimations follow the WTC method à la Torrence and Compo (1998), with adjustments of Grinsted et al. (2004), and Ng and Chan (2012), including the phase difference. Significant heterogeneity in terms of COVID-19 restrictive policies is observed across Eurocontrol countries. Therefore, the WTC is performed at the Eurocontrol aggregate level and for each country separately.

4. Results

The descriptive statistics of the raw variables are presented in Table A1 (Appendix), while Table A2 (Appendix) shows the results of the Portmanteau test for white noise. The tests indicate that no white noise is observed in the considered variables, with estimations not suffering from bias.

Fig. 3 shows the WTC plot of the co-movement between log(Pandemic) and log(AT), from 01/03/2020 to 31/12/2021, at the Eurocontrol aggregate level. The thick black contour reveals the 5% significance level, while the cone of influence (COI) indicates the regions where the edge effects might distort the picture being described as a lighted shadow. WTC is estimated based on Monte Carlo simulations by using phase randomised surrogate series.

Fig. 3.

WTC of co-movement between log(Pandemic) and log(AT).

The intensity of interaction between variables is indicated by the power range colour that goes from blue (low power, low intensity of interaction) to yellow (high power, high intensity of interaction). The orientation of the arrows indicates the phase difference between the series and their lead-lag status. Therefore, the variables have the same sign when the arrows are oriented to the right, they experiencing the same co-movement (i.e. positively linked/with cyclical effects). In this case, the log(Pandemic) is leading when arrows are oriented to the right and up (i.e. the direction of co-movement runs from pandemic to air transportation), while log(AT) is leading when arrows are oriented to the right and down (i.e. the direction of co-movement runs from air transportation to pandemic).

Otherwise, the variables have the opposite sign exhibiting a contrary co-movement (i.e. negatively linked/with anti-cyclical effects) when the arrows are oriented to the left. Herein, the Log(Pandemic) is leading when arrows are oriented to the left and down (i.e. the direction of co-movement runs from pandemic to air transportation), while log(AT) is leading when arrows are oriented to the left and up (i.e. the direction of co-movement runs from pandemic to air transportation).

The duration of co-movement is related to the bands of scale, being conventionally split into four time-horizons. Concretely, they range from very short- (up to 10 days band of scale, as very high frequency), short- (10–30 days band of scale, as very high frequency), medium- (i.e. 30-90 days band of scale, as medium frequency) to long-term (i.e. more than 90 days band of scale, as low frequency).

The plot evidences interesting information in the very short-term (i.e. very high frequency), up to 10 days band of scale. Herein, although the co-movements between log(Pandemic) and log(AT) are rather idiosyncratic up to 4 days band of scale, six sub-periods are clearly filtered by the wavelet tool at 5–10 days band of scale.

The first sub-period is related to the debut of the pandemic and covers April–June 2020. The arrows are pointed to the right and down, with log(AT) positively leading log(Pandemic). In this sub-period, air traffic slowly recovers after the lockdown due to cargo (Wood and Knowles, 2022) and medical or repatriation flights (Karim et al., 2020). The positive co-movement allows one to suspect air transportation as a potentially spread environment, possibly because of weaknesses in preventive pandemic procedures during traffic operations for both employees and passengers. Low COVID-19 Containment and Health Index levels at the beginning and end of this period support this finding (Figure A2, Appendix). The result fully confirms Fareed et al. (2022) for exactly the same sub-period and band of frequency.

The novelty and unknowns of the COVID-19 virus are two essential characteristics of the pandemic's debut. Noteworthy is that the number of tests is low at the beginning and progressively increases starting with May 2020, with a maximum level in March 2021, as Figure A2 (Appendix) shows. The same figure reveals that the number of vaccinations substantially grows with January 2021, with two maximum points in June and December 2021 and a minimum level in October 2021. Figure A2 (Appendix) also illustrates that the COVID-19 Containment and Health Index, which captures the intensity of COVID-19 policy response, steeply increases in April–May 2020 and relaxes in June–July 2020, with a smoothed level remaining until October 2020. A new slight increase is observed in November 2020, remaining at this level until May 2021. From May to July 2021, the intensity of the COVID-19 policy response relaxes, smoothly evolving at this magnitude until December 2021.

A second sub-period emerges over August–September 2020. As the arrows are oriented to the right and up, log(Pandemic) positively leads log(AT). Despite concern regarding the new Alpha and Beta virus variants (i.e. September 2020), the EU zone has been less affected. Even so, the pandemic continuously spreads, accompanied by a curious increase in air traffic, with its first peak after the generalise lockdown (Fig. 1). Although the pandemic extends, the demand for flights is explained by the social mobility needs after the long period of isolation, summer holiday pressure and intensification of commercial flights (Wood and Knowles, 2022; Karim et al., 2020). More relaxed COVID-19 regulations and just a slight tightening of mask use rules are also observed in this sub-period (Figure A2, Appendix).

Further, a third sub-period is observed over October–November 2020, with the arrows pointed to the right and down, and log(AT) positively leading log(Pandemic). Air traffic seems to support the pandemic disease along with other specific spread factors, and with new COVID-19 cases exploding at the end of the year.

The fourth sub-period debuts in January 2021, with arrows oriented to the right and up, and log(Pandemic) positively leading log(AT) over January–June 2021. Despite the pandemic spread and fear of newly observed Gamma and Delta variants (i.e. December 2020), air traffic maintains an increasing trend, especially because of accelerated testing and, more importantly, newly imposed rules, with the mandated start of the vaccination campaign. Herein, the adapted intensity of the COVID-19 policy responses is consistently kept, as Figure A2 (Appendix) shows.

The fifth sub-period covers July–August 2021, with arrows now pointing to the left and up, and log(AT) negatively leading log(Pandemic). Herein, the spread of COVID-19 through air traffic activities is drastically reduced as the effects of the previous vaccination campaign, the vaccine becoming mandatory in almost all ground, in-flight or adjacent specific air transportation activities for both passengers and employees. Therefore, the need for social mobility and working activities in the air sector seems to be a great stimulus for vaccination but with a delay effect. Curiously, the attenuated vaccination campaign in this sub-period seems to be strongly compensated by testing revival in parallel with other prevention responses (Figure A2, Appendix). All of these events, plus the effect of the vaccination campaign, induce a pandemic spread ‘plateau’ in the second part of the considered sub-period, as Fig. 1 shows.

In the sixth sub-period, log(Pandemic) positively leads log(AT) over September–December 2021 (i.e. arrows pointed to the right and up). Air traffic maintains a constant dynamic despite the proliferation of the virus and the identification of the new Omicron variant (i.e. November 2021). The rules in terms of testing and vaccination significantly expanded (i.e. the vaccination campaign reached its second peak in December 2021), and policy responses slightly increased (Figure A2, Appendix).

In the short-term (i.e. high frequency), at 10–30 days band of scale, the wavelet tool nicely filtered one sub-period, covering November 2020–March 2021. In this case, log(Pandemic) positively led log(AT) as the arrows are pointed to the right and up. Herein, the testing procedures and vaccination campaign, with its first peak in June 2020, substantially supported the air sector.

Finally, two sub-periods are evidenced in the medium-term (i.e. medium frequency), at 30–90 days band of scale. The first covers March–August 2020, while the second is related to October–December 2021.

In the first sub-period, log(Pandemic) negatively leads log(AT), while the direction changes as the frequency slightly increases (i.e. the arrows are oriented to the left and down, and then to the left and up but for a very short sequence). This highlights the collapse of air traffic in the medium-term because of the pandemic generalised lockdown from April 2020 and broad concern. The finding is consistent with Fareed et al. (2022) for the same band of frequency and sub-period.

The second sub-period is characterised by log(AT) positively driving log(Pandemic), with the arrows pointing to the right and down. This reinforces the idea that air transportation can be a source of pandemic spread in the medium-term, despite adapted ground and in-flight preventive procedures, especially during intensive pandemic spread (i.e. end of 2021). Figure A2 (Appendix) clearly shows quite relaxing policy responses compared with the debut of 2021.

The types of flights can significantly influence all co-movements revealed by the WTC in Fig. 3. Therefore, this potential sensitivity is analysed based on the WTC tool related to the pandemic and passenger, cargo and other types of flights, as Fig. 4, Fig. 5, Fig. 6 show. Unfortunately, this endeavour is dictated by the dataset availability, missing official observations for the period 07/02/2021-31/12/2021. Nevertheless, several interesting findings are noteworthy.

Fig. 4.

WTC of co-movement between log(Pandemic) and log(ATP).

Fig. 5.

WTC of co-movement between log(Pandemic) and log(ATC).

Fig. 6.

WTC of co-movement between log(Pandemic) and log(ATP).

The results derived from Fig. 4 are robust to Fig. 3, underlining the dominance of passenger flights on total flights (Eurocontrol, 2021). The co-movements related to the pandemic and cargo flights are shown in Fig. 5, with the arrows pointed to the right and down in the very-short term (i.e. very high frequency), at 5–10 days band of scale. Herein, log(ATC) positively leads log(Pandemic), indicating that the cargo flights spread COVID-19. This fully fits the outputs of WTC in Fig. 3, with the exception of the sub-period August–September 2020, characterised by high pressure for passenger flights, as shown by the second sub-period in Fig. 3. The finding suggests that the pandemic rules related to cargo air flights seem to be superficially respected by ground workers and less persuasively followed by crewmembers. By comparison, passenger flights boost the responsibility of aviation employees.

Fig. 6 is devoted to the link between the pandemic and other flights, replicating the previous results also in the very-short term (i.e. very high frequency), at 5–10 days band of scale. Unlike previous types of flights, intensive and positive co-movements are also observed here in the medium-term (i.e. medium frequency), at 30–90 days band of scale, until August 2020. With the arrows preponderantly oriented to the right and up, the log(Pandemic) positively leads log(ATO). This indicates that the pandemic positively runs air transportation related to the other flights, in contrast with the first sub-period of the WTC in Fig. 3 (i.e. medium-term, over March–August 2020, at 30–90 days band of scale). Herein, the necessity for special flights (i.e. flights for repatriations, business jet flights, ambulance flights, government flights, military flights, etc.) is more than acute, being required by the pandemic debut as much as COVID-19 spreads worldwide.

Unfortunately, significant heterogeneity across Eurocontrol countries can also be observed regarding COVID-19 applied prevention responses, as shown in Figure A3. Countries such as Italy, Greece, Morocco, and Cyprus are characterised by strong COVID-19 policy responses in contrast with Estonia, Bosna and Herzegovina, and Finland, which experienced more relaxed rules.

To test the importance of those differences in ‘pandemic - air traffic’ nexus, separate WTC plots are employed for each country (Figure A4-A44, Appendix). The plots show some interesting findings. They illustrate that the co-movements between the pandemic and air traffic are generally weak in the countries with a low level of infections and reduced air traffic, as is characterised by fewer air connections. Herein, the co-movements are either idiosyncratic or predominantly dominated by the colour blue, suggesting occasional (or no) lead-lag status. This group includes Albania, Armenia, Bosnia-Herzegovina, Cyprus, Denmark, Georgia, Ireland, and Malta. Those countries are characterised by quite reduced pandemic spread and low air traffic, as Figure A45 reveals. At the opposite pole are countries with a high spread of disease and intensive air traffic, most of which are hub-countries. Germany, France, the United Kingdom, Spain, Turkey and Italy dominate this group, as Figure A45 illustrates. Their related WTC plots show that there are strong co-movements between the pandemic and air traffic, proved by extended intensive yellow areas comparable with those from Fig. 3. This highlights the idea that the expanded disease spread and intensive traffic are two important attributes in hub-countries that shape the pandemic - air traffic link.

All of these circumstances suggest that the baseline findings attached to Fig. 3 better characterised the hub-countries, with extended pandemic spread and intensive air traffic, with policy responses playing an essential role in the link between the pandemic and air traffic.

Unlike many studies, this finding reveals that the connection between the COVID-19 pandemic and air transportation is observed only for specific sub-periods of time and different bands of frequency, registering both directions of co-movements (i.e. pandemic to air transportation and air transportation to pandemic).

The main turning points seem to be relevantly linked with the introduction/expansion of COVID-19 diagnostic tests, advances in vaccination campaigns, and the consistency of other specific COVID-19 preventive procedures (e.g. contact tracing and face coverings accompanied by connection facilities, screening procedures, boarding methods and/or in-flight rules).

Moreover, those co-movement changes are generally related to the short-term, coinciding with the virus incubation period. This is in accord with Paul and Lorin (2021), and WHO (2021), who indicate a COVID-19 incubation period of an average of 5–6 to 14 days. General concerns and experience in preventive procedures are defining for the medium-term. Not least, the findings are robust to passenger flights and very sensitive to the cargo or other types of flights, the country's pandemic context and preventive approach.

5. Robustness check

A robustness check is performed at the Eurocontrol aggregate level based on (a) an alternative method to WTC and (b) a set of control variables that allows for isolating the effect of ‘COVID-19 pandemic - air transportation’ interactions.

• (a)\ Wavelet cohesion (WC), developed by Rua (2010), is alternatively used to analyse the co-movement between the COVID-19 pandemic and air transportation. Compared with the WTC, which represents “the absolute value squared of the smoothed cross-wavelet spectrum, normalised by the smoothed wavelet power spectra” (Rua and Nunes, 2009, p. 634), the WC evidences the “contemporaneous correlation coefficient around each moment in time and for each frequency” (Rua, 2010, p. 687). The co-movement measure proposed by Rua (2010) is ${\rho }_{x_n{y}_n}\text{,}$ represents a real number on [-1, 1]:

$${\rho }_{x_n{y}_n}=\frac{\mathfrak{R}\left(W_n^x{W}_n^y\right)}{\sqrt{{\left|W_n^x\right|}^2{\left|W_n^y\right|}^2}}\text{,}$$ (5)

Rua's (2010) construct is based on WTC, but uses only the real part of wavelet cross-spectra, capturing the negative correlations as a novelty.

Figure A46 (Appendix) plots the WC of co-movement between log(Pandemic) and log(AT), fully reinforcing the outputs of WTC. The intensity of co-movement is suggested by colours, the power ranges going from intense blue colour (high negative co-movement) to intense yellow colour (high positive co-movement). Although the WC does not offer information about the lead-lag status of the variables, their cyclical and anti-cyclical effects are clearly evidenced. The results remain robust in the very short-term, at the 5–10 days band of scale, where the intense yellow colour indicates a strong positive co-movement between log(AT) and log(Pandemic) over April–June 2020, October–November 2020, and July–August 2021. Similar positive links are observed in the very short-term over August–September 2020, January–June 2020, and September–December 2021. In the short-term, at the 20–40 days band of scale, WC reinforces the filtered sub-period by WTC over November 2020–March 2021, when log(Pandemic) is in phase with log(AT). Finally, in the medium term, at 30–90 days band of scale, WC also confirms both WTC identified sequences: March–August 2020, with a negative sign, and October–December 2021, with a positive one.

• (b)A set of control variables is entered to isolate the effect of interaction between the Pandemic and AT, including the Tests, Vaccinations, CPR, OFR, Brent and STOXX related to the aviation industry.

As WHO (2022, p. 1) states, COVID-19 testing is essential to a comprehensive COVID-19 response strategy, while vaccinations have a high propensity to reduce SARS-CoV-2 transmission and infection, as Wald (2022) claims. In parallel, Chung et al. (2021) highlight the role of policy responses to mitigate the pandemic spread through various other specific measures in the absence of a vaccine or effective treatment.

Financial stress plays a crucial role in the air transportation industry, especially during the COVID-19 pandemic (Shi and Li, 2021), while the oil price is significant due to its influence on stock prices and volatility in the air industry (Yun and Yoon, 2019). Additionally, IATA (2020) predicted steep air industry losses in 2021, despite a slight improvement in terms of performance throughout the forecast.

The multiple and partial wavelet coherency (MWC and PWC) tools of Mihanović et al. (2009) facilitate inserting the controls. More precisely, the MWC allows for analysing the influence of a vector of independent variables (x ₁ , x ₂ , … x _n) on a dependent one (y). Considering two vector variables x ₁ and x ₂, the squared MWC has this form:

$${\left({RM}_n^{y{x}_1{x}_2}\right)}^2=\frac{{\left({RM}_n^{y{x}_1}\right)}^2+{\left({RM}_n^{y{x}_2}\right)}^2-2Re\left({RM}_n^{y{x}_1}{RM}_n^{y{x}_{2*}}{RM}_n^{y{x}_{1*}}\right)}{1-{\left({RM}_n^{x_2{x}_1}\right)}^2}\text{,}$$ (6)

where y represents the impacted variable (i.e. log(AT), in our case), while x ₁ and x ₂ are the explanatory variables (i.e. interest variable log(Pandemic) - x ₁, and control variables log(Tests), log(Vaccinations), log(CPR), log(OFR), log(Brent) or log(STOXX) - x ₂). The squared PWC is as follows:

$${\left({RP}_n^{y{x}_1{x}_2}\right)}^2=\frac{{\left|{RP}_n^{y{x}_1}-{RP}_n^{y{x}_2}{RP}_n^{y{x}_{1*}}\right|}^2}{{\left[1-\left({RP}_n^{y{x}_2}\right)\right]}^2{\left[1-\left({RP}_n^{x_2{x}_1}\right)\right]}^2}\text{.}$$ (7)

The PWC allows for analysing the co-movement between two time series y and x ₁ , after removing the influence of the third one x ₂.

MWC and PWC plots of co-movement between log(Pandemic) and log(AT) by controlling for log(Tests), log(Vaccinations), log(CPR), log(OFR), log(Brent), and log(STOXX) are presented in Figures A47-58 (Appendix). The intensity of correlations between variables is shown by colour, going from blue (low correlation) to yellow colour (high correlation).

MWC plots illustrate that all the control variables significantly contribute to the ‘log(Pandemic) - log(AT)' nexus, with their actions extending the link effects over both frequencies and sub-periods (i.e. yellow colour zones are visibly extended). Herein, noteworthy is that the log(CPR), log(OFR), log(Brent) and log(STOXX) variables also exert a medium-to long-term effect at more than 120 days band of scale (i.e. low frequency). This, importantly, unveils that the COVID-19 policy response and economic disruption in the air sector are expected to be observed around 4 months after the pandemic shock.

The results generally remain robust regarding the co-movement by removing their influence, with a few interesting exceptions in the very-short term (i.e. 5-10 days band of scale), as the PWC plots show: log(Tests) and log(Vaccinations). Herein, by removing the log(Tests) and log(Vaccinations), the link ‘log(Pandemic) - log(AT)' entirely disappears for the whole period in the case of log(Tests) and partially for log(Vaccinations), with the debut of vaccination campaign (i.e. January 2021). This indicates that the co-movements are very sensitive to tests and vaccinations, highlighting their crucial role in the air sector for managing flights during the pandemic disease. This is in line with WHO (2022) and Wald (2022).

Regarding log(CPR), log(OFR), log(Brent) and log(STOXX), the observed medium-to long-term effect disappears by removing these variables. This highlights their significant contribution to the ‘log(Pandemic) - log(AT)' nexus in the medium-to long-term. Herein, CPR highlights the influence of policy responses on air transportation during COVID-19, being consistent with Chung et al. (2021) and Sun et al. (2021). Such measures refer to school closures, workplace closures, travel bans, contact tracing or face coverings, in parallel with connection facilities, screening procedures, boarding methods and/or in-flight rules. OFR thoroughly explains the uncertainty valence of the new COVID-19 pandemic and its financially induced emotional reactions (Figure A59, Appendix), significantly affecting the air sector, especially at the beginning of the disease. Otherwise, the supply chain disruption during the lockdown and the alteration of the global socio-economic context induced high volatility and a sharp rise of the Brent price in 2021 (Figure A59, Appendix), substantially influencing the air transportation sector. Moreover, supply chain issues and a fall in air transportation demand negatively affected the performance of the air sector, initially worsening the STOXX index (Figure A59, Appendix), with further impact on ‘log(Pandemic) - log(AT)' co-movement. Those outputs confirm the findings of IATA (2020), Yun and Yoon (2019), and Shi and Li (2021).

To sum up, the results are generally robust to the alternative wavelet tool but are sensitive to tests and vaccinations in the very short-term as well as to other specific policy responses, financial stress conditions, oil prices and performance of the aviation industry in the medium-to long-term.

The study has several limits. First, the analysis does not discriminate between passenger, cargo and other types of flights for the entire considered period because of a lack of dataset starting with February 2021. Second, although car and maritime, but especially train transportation, significantly compete with the air one (Eurocontrol, 2009), for objective reasons, no such additional controls are used to isolate the co-movement between the interest variables. More precisely, there is no dataset officially available with daily frequency to capture those transportation variables. Third, as wavelet is very sensitive to the quality of the datasets used, their conversion from higher to lower frequency (i.e. from semi-annual to quarterly, semi-annual to monthly, quarterly to monthly etc.) can generate biases, altering the accuracy of estimations. Finally, no dataset is available regarding the specific internal air policy responses better to explain the connection between the pandemic and air traffic.

6. Conclusions

The paper uses wavelet methodologies to analyse the co-movement between the COVID-19 pandemic and air transportation. The study covers the period from 01/03/2020 - 31/12/2021 at the Eurocontrol level.

The main findings show that the lead-lag status of the ‘pandemic - air transportation’ nexus is contextual, significantly varying across time and frequency. The notable co-movements between the pandemic and air transportation are confined to the very short-term, coinciding with the virus incubation period. The intensity and direction of interaction depend on the consistency of preventive procedures or the extent of testing and vaccination. Both tests and vaccinations are the ‘golden rule’ in supporting air transportation during periods of pandemic disease. Interestingly, the pandemic is leading especially during periods characterised by the smooth evolvement of policy responses, irrespective of their magnitude. Otherwise, air traffic is generally leading under weak preventive pandemic procedures or during pandemic spread ‘plateau’, with testing and vaccination having different trends. Moreover, compliance with pandemic rules seems to be superficial in cargo and other types of flight operations compared with passenger ones, with passenger flights increasing the responsibility of aviation employees.

Under general pandemic concern, the effects of lockdown measures on air transportation are exclusively observed in the medium-term, with a strong negative impact on flights. In parallel, an expansion of air traffic accompanies the pandemic spread in this period, being required by objective needs (i.e. flights for repatriations, business jet flights, ambulance flights, government flights, military flights, etc.). On the same horizon, despite all prevention measures, air transportation seems to become a good pandemic ‘spreader’, especially during the pandemic peak. All these findings generally characterise the hub-countries, strongly affected by the disease, with high air traffic. Financial stress, oil prices and performance in the air industry are defining 'binders' for the ‘pandemic - air transportation’ nexus in the medium-to long-term.

Regarding policy implications, it is required for policymakers to adapt their adjustments in the very short-term based on the pandemic dynamic. Encouraging testing and the acceleration of vaccination, in parallel with other preventive measures (i.e. contact tracing, face coverings, ground social distancing, connection facilities, screening procedures, boarding methods and/or in-flight rules), are crucial 'ingredients' for air transportation sustainability during pandemic crises. Special attention should be paid to compliance with the pandemic rules in the case of employees involved in cargo and other types of flights by imposing additional supervising procedures.

In the medium-term, lockdown periods with strong emotional ‘touch’ are of high interest, with restrictive flight conditions having a significant impact on air transportation. Oil prices and the performance of the air sector should be carefully monitored in the medium-to long-term as well. Policymakers should be prepared to counteract the increase in oil prices after the outbreak when the global air transportation demand progressively decompresses while various facilities for the air industry should also prevail to attenuate the reduction of aircraft demand during the disease peaks. The above policy corrections better fit the hub-countries, which are characterised by high air traffic and widespread pandemic disease.

As for further research, extending the study to North America and Asia is more than welcome since those regions are also characterised by high air traffic density and have been strongly affected by recent pandemic shocks. Depending on the dataset availability, a comparison between different types of transportation and their interaction with the COVID-19 pandemic can be considered as well.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix.

Table A1.

Descriptive statistics of raw variables (Eurocontrol aggregate level)

Variable	Mean	Median	Maximum	Minimum	Std. Dev.	Sum	Sum Sq. Dev.	Obs.
AT	14445.8	13542	27613	2099	6596.165	9693135	2.92E+10	671
ATP	9929.997	9521	26550	1549	5275.932	3405989	9.52E+09	343
ATC	911.1983	1003	1317	330	262.222	312541	2.35E+07	343
ATO	216.2187	220	375	41	70.96949	74163	1722541	343
Pandemic	8513.339	7313.359	52355.26	14.173	7700.045	5712450	3.97E+10	671
Tests	178.381	192.425	670.155	0.105	124.2864	119693.7	10349564	671
Vaccinations	1461401	734928	6949647	0	1751337	9.81E+08	2.06E+15	671
CPR	57.95845	55.16	69.69947	13.925	8.725662	38890.12	51011.91	671
OFR	−1.78426	−3.015	10.266	−4.364	2.950689	−1197.24	5833.399	671
Brent	55.89872	55.76	85.76	9.12	18.38929	37508.04	226571.2	671
STOXX	1474.86	1545.48	1829.18	916.2	233.0778	989631.3	36397910	671

Table A2.

Portmanteau tests for white noise (Eurocontrol aggregate level)

Variable	Portmanteau (Q) statistic	Prob > chi2
log(AT)	15760.90	0.0000
log(ATP)	5640.43	0.0000
log(ATC)	3562.88	0.0000
log(ATO)	3547.15	0.0000
log(Pandemic)	16061.90	0.0000
log(Tests)	16716.89	0.0000
log(Vaccinations)	23729.49	0.0000
Log(CPR)	5248.97	0.0000
log(OFR)	20219.83	0.0000
log(Brent)	20719.20	0.0000
log(STOXX)	19326.66	0.0000

Note: variables Pandemic and WTI have been rescaled in order to obtain strict positive values.

Fig. A1.

Density of world air traffic.

Source: www.flightradar24.com - screenshot, November 04th, 2022, 11h00 AM (CET)

Fig. A2.

New COVID-19 tests, vaccinations, and COVID-19 Containment and Health Index in Eurocontrol zone over 01/03/2020 - 31/12/2021.

Sources: performed based on datasets freely offered by the Our World and Data, 2022c, Our World and Data, 2022d, Our World and Data, 2022b.

Fig. A3.

Covid-19 Containment and Health Index in Eurocontrol zone as average per country (2020–2021).

Sources: performed based on datasets freely offered by the Our World in Data (OWD) (2022d).

Fig. A4.

WTC of co-movement between log(Pandemic) and log(AT) - Albania

Fig. A5.

WTC of co-movement between log(Pandemic) and log(AT) - Armenia

Fig. A6.

WTC of co-movement between log(Pandemic) and log(AT) - Austria

Fig. A7.

WTC of co-movement between log(Pandemic) and log(AT) - Belgium

Fig. A8.

WTC of co-movement between log(Pandemic) and log(AT) - Bosnia and Herzegovina

Fig. A9.

WTC of co-movement between log(Pandemic) and log(AT) - Bulgaria

Fig. A10.

WTC of co-movement between log(Pandemic) and log(AT) - Croatia

Fig. A11.

WTC of co-movement between log(Pandemic) and log(AT) - Cyprus

Fig. A12.

WTC of co-movement between log(Pandemic) and log(AT) - Czech Republic

Fig. A13.

WTC of co-movement between log(Pandemic) and log(AT) - Denmark

Fig. A14.

WTC of co-movement between log(Pandemic) and log(AT) - Estonia

Fig. A15.

WTC of co-movement between log(Pandemic) and log(AT) - Finland

Fig. A16.

WTC of co-movement between log(Pandemic) and log(AT) - France

Fig. A17.

WTC of co-movement between log(Pandemic) and log(AT) - Georgia

Fig. A18.

WTC of co-movement between log(Pandemic) and log(AT) - Germany

Fig. A19.

WTC of co-movement between log(Pandemic) and log(AT) - Greece

Fig. A20.

WTC of co-movement between log(Pandemic) and log(AT) - Hungary

Fig. A21.

WTC of co-movement between log(Pandemic) and log(AT) - Ireland

Fig. A22.

WTC of co-movement between log(Pandemic) and log(AT) - Israel

Fig. A23.

WTC of co-movement between log(Pandemic) and log(AT) - Italia

Fig. A24.

WTC of co-movement between log(Pandemic) and log(AT) - Latvia

Fig. A25.

WTC of co-movement between log(Pandemic) and log(AT) - Lithuania

Fig. A26.

WTC of co-movement between log(Pandemic) and log(AT) - Luxembourg

Fig. A27.

WTC of co-movement between log(Pandemic) and log(AT) - Malta

Fig. A28.

WTC of co-movement between log(Pandemic) and log(AT) - Moldova

Fig. A29.

WTC of co-movement between log(Pandemic) and log(AT) - Morocco

Fig. A30.

WTC of co-movement between log(Pandemic) and log(AT) - Netherlands

Fig. A31.

WTC of co-movement between log(Pandemic) and log(AT) - North Macedonia

Fig. A32.

WTC of co-movement between log(Pandemic) and log(AT) - Norway

Fig. A33.

WTC of co-movement between log(Pandemic) and log(AT) - Poland

Fig. A34.

WTC of co-movement between log(Pandemic) and log(AT) - Portugal

Fig. A35.

WTC of co-movement between log(Pandemic) and log(AT) - Romania

Fig. A36.

WTC of co-movement between log(Pandemic) and log(AT) - Serbia

Fig. A37.

WTC of co-movement between log(Pandemic) and log(AT) - Slovakia

Fig. A38.

WTC of co-movement between log(Pandemic) and log(AT) - Slovenia

Fig. A39.

WTC of co-movement between log(Pandemic) and log(AT) - Spain

Fig. A40.

WTC of co-movement between log(Pandemic) and log(AT) - Sweden

Fig. A41.

WTC of co-movement between log(Pandemic) and log(AT) - Switzerland

Fig. A42.

WTC of co-movement between log(Pandemic) and log(AT) - Turkey

Fig. A43.

WTC of co-movement between log(Pandemic) and log(AT) - Ukraine

Fig. A44.

WTC of co-movement between log(Pandemic) and log(AT) - United Kingdom

Fig. A45.

New COVID-19 cases per million per day and total flights per day in Eurocontrol zone (average, 2020–2021).

Sources: performed based on datasets freely offered by the Our World in Data (OWD) (2022a), and Eurocontrol (2022).

Fig. A46.

WC of co-movement between log(Pandemic) and log(AT)

Fig. A47.

MWC of co-movement between log(Pandemic) and log(AT) - log(Tests) as control

Fig. A48.

PWC of co-movement between log(Pandemic) and log(AT) - log(Tests) removed

Fig. A49.

MWC of co-movement between log(Pandemic) and log(AT) - log(Vaccinations) as control

Fig. A50.

PWC of co-movement between log(Pandemic) and log(AT) - log(Vaccinations) removed

Fig. A51.

MWC of co-movement between log(Pandemic) and log(AT) - log(CPR) as control

Fig. A52.

PWC of co-movement between log(Pandemic) and log(AT) - log(CPR) removed

Fig. A53.

MWC of co-movement between log(Pandemic) and log(AT) - log(OFR) as control

Fig. A54.

PWC of co-movement between log(Pandemic) and log(AT) - log(OFR) removed

Fig. A55.

MWC of co-movement between log(Pandemic) and log(AT) - Brent as control

Fig. A56.

PWC of co-movement between log(Pandemic) and log(AT) - Brent removed

Fig. A57.

MWC of co-movement between log(Pandemic) and log(AT) - log(STOXX) as control

Fig. A58.

PWC of co-movement between log(Pandemic) and log(AT) - log(STOXX) removed

Fig. A59.

OFR, Brent and STOXX over 01/03/2020 - 31/12/2021.

Sources: performed based on datasets freely offered by the Office of Financial Research database (2022), Energy Information Administration of United States online database (2022) and STOXX Europe Total Market Aerospace & Defense Index, Qontigo online database (2023).

Data availability

Data will be made available on request.