Recovery Period of Air Transportation: Vector Error Correction Model

Air transportation has two signi�cant modules named air passenger and freight. Air transport is the primary module of civil aviation and because of its nature, air transport has been simultaneously affected by Pandemics and crises. Gulf Crisis, 9/11, 2008–2009 Financial Crisis, SARS, and MERS Pandemics harm air transport, however, the in�uence of COVID-19 was more devastating than the other Pandemics and crises due to its global effect. This effect has continued a long period that still this effect exists now with a slight trend. The aim of this study is to analyse the selected variables that shows the past and future trend of air transportation related to operational and �nancial status. These variables are the primary ones that can de�ne the countries' general status in air transport. The forecasting results are examined by 9-months forecasting with Vector Error Correction Model. It is forecasted that slightly decreasing trend will proceed in the following 9-months for passenger transportation due to fall and winter seasons. It is forecasted that slightly upward trend will proceed in the following 3-months and slightly decreased in the other 6-months for cargo transportation due to potential economic crisis in 2023. The originality of this paper is the �rst research related to analyse passenger and freight transportation together with the operational and �nancial parameters that de�ned in the sample of data and methodology sections.


Introduction
Air transportation is a staminal facilitator for the countries' development.Air transportation includes air passenger and air freight modules.Especially air passenger module is related to the economic status and welfare of people.Trade and tourism primarily affect the country's development rates, so the development of air passenger transportation increases revenues with the development interest of demanded services in high amounts (Schäfer and Waitz, 2014).This study forecasts the following three quarters (9-month period) to analyse the negative impact of COVID-19 on air transportation.When time passes and the COVID-19 effect has decreased, air passenger demand will probably rise, and the growing trend of civil aviation will rise too.Nearly all countries prohibited travel to other countries because of the increment in COVID-19 cases.Several strategies regarding restrictions and procedures have been applied in countries, so air passenger tra c numbers decreased (Lau et al. 2020b).COVID-19 impacted nearly all industries globally by affecting their nancial conditions.After COVID-19 had appeared in Wuhan on 27 December 2019, World Health Organization (WHO) accepted it as a global Pandemic.The widespread anxiety about COVID-19 is the biological condition of this virus and public health.As time passes, the spreading of COVID-19 and dead numbers also decreased due to the mutated viruses and the speed of the vaccination process (Huang et al. 2020;Ruan et al. 2020).
The countries noti ed more inhibitive measures to restrict the contagion of this virus, so these measures ended with a stunning decrease in air transportation demand "never seen before" outcomes.The rst peak of COVID-19 happened between 1 March and 1 June 2020.It ended up with approximately 17,000 aircraft being out of service.This immense demand shrinkage cut back the operations in all industries covering the airports and aircraft manufacturers that faced a signi cant decline in their supplies (Amankwah-Amoah, 2020; Macilree and Duval, 2020; Serrano and Kazda, 2020; Sun et al. 2020).The annual development rate of the civil aviation industry in 21st century has 4.2%.More than 5000 airlines and 40 million ights clearly show that the global airline market value is measured by billions of dollars (USD). Furthermore, civil aviation affects the Gross Domestic Product (GDP) by more than 1% globally (IATA, 2020a).So, the importance of civil aviation is better than the other transportation modules.Nowadays, there have more than 1200 big-scale international airports globally and these airports provide the transportation of more than 4 billion passengers annually (IATA, 2020c).
Besides air passenger, air freight is described as the transportation process of products by using an air carrier.Air freight is evaluated as an important transportation module when these goods are carried globally (Air Freight, 2022).Air transportation has a signi cant development trend globally, so the revenues and populations have increased with the alteration of industrial structure.This status has affected the progress of free trade which enhanced this development trend globally (Alekseev and Seixas, 2009).With the development of air freight transportation demand, air tra c models have also altered and turned into a more complicated structure (Xie et al. 2014).Air tra c models are related to air transportation and include aircraft, airports, ight destinations, planning of passenger and freight by using air.Air transportation also affects the social and economic development of countries.Besides air transportation, the air freight industry has a complicated structure with nearly doubled its volume in 10 years period from 1970 to 2005 (Chang et al. 2007).International Air Transport Association (IATA) published a document about the rst ve-year period of air freight carriers in the 21st century.This document speci ed that this transportation module accounted for 36% of the total freight value and this value has been on an increasing trend (IATA, 2006).In the rst peak of the 2000s, air freight transportation developed approximately 50% faster than passenger transportation between 1995 and 2004 with a growing trend.This development trend continued after the 9/11 and 2003 Financial Crises because this growing trend also negatively affected air freight transportation with lower ratio and time period than air passenger transportation (Wong et al. 2009).
The pro t level of this transportation module reached 40% in 2009, while this pro t was only 5% in 2000 (Han et al. 2010, Nobert andRoy, 1998).In 2014, Boeing Company (2014) forecasted that the air freight industry has proceeded to develop by a 4.7% per year.The forecasts show that this number will triple its income in 2033.The estimations speci ed that from 2013 to 2033, the billion ton-kilometers (RTKs) have risen from 207.8 to 521.8.There have several strategies for the sustainability of the stunning development of expanding international trade (Li et al. 2009, Ou et al. 2010).So, airlines take place in the operation process of air freight.They enhance their strategic plans to re ect changes in the global competitive landscape (Nobert and Roy, 1998;Ferguson et al. 2013).Thus, increasing theoretical research have tried to solve the di culties in the operational process in air freight since the 1990s (Feng et al. 2015).Besides, there was a general supposition about the global aviation industry with an improvement trend in 2020.So, the status was the same as the growing years that has in a consecutive growth in air passenger, freight, and incomes in the latest years.Following this developing pattern, several airlines have made investments in purchasing and leasing more aircraft from well-known manufacturers like Airbus and Boeing, offering signi cant savings on new orders with long-term contracts (IATA, 2020b).
In addition to these de nitions related to air passenger and air freight transport, this study aims to analyze the 11 variables that mentioned below according to all active countries.These variables are; In this study, these 11 variables are gathered to gure out signi cant factors that de ne the operational and nancial level of air transport (passenger and freight) for countries.This study also analyzes the COVID-19 effect on air passengers and air freight transport (not affected as passenger transportation) as an unprecedented worldwide crisis globally.

Literature Review
When it is examined the related studies, rst study is related to predict the relationship between the degree of economic shocks and the temporal recovery of the global air transport business was published by Gudmundson et al. (2021).According to this study's results, the global ight demand, particularly for passengers, will take at least 2.4 years (recovery by the end of 2022) to reach pre-COVID-19 levels.The most optimistic forecast for the recovery has continued approximately two years (recovery by the third quarter of 2022), while the most pessimistic forecast for the recovery has continued approximately for six years (recovery in 2026).According to the methodology related to passenger and freight transportation, the recovery period forecast calculated by using a univariate approach called ARIMAX [12].This study was published at the beginning of 2021, so the recovery is not re ecting the up-to-date data at.Second study is related to air travel was released by Truong (2021).Truong analysed the quantity of both domestic and foreign ights.This study speci ed that although the number of ights during the pandemic may not have reached 2019 levels, in 2022, the number of ights will not far away about the demand for travel in 2019.In that research, neural network models for estimating domestic and international air transportation in the medium and long terms were developed and tested.In order to estimate passenger demand, economic factors following COVID-19 that placed restrictions on transportation were examined.In the third study, Wang and Gao (2021) analyzed 87 research about air transportation.They took these studies between 2010 to 2020.They used preliminary analytical techniques to analyze the input data.In the input data, three analyses were created and collected.This analysis revealed the relationship between the reviewed studies By forecasting airlines' socioeconomic and operational characteristics in time series modelling, the study reviewed air transportation demand on international scale.
In the fourth study, Dube et al. (2021) speci ed that because of air travel is in full swing, general problems will not resolve right away.He proposed to aviation specialists that safeguarding passengers' health and safety, planning ticket prices, boosting e ciency, ensuring high-quality in-ight amenities, and maintaining such safeguards is likewise essential for the development of air tra c.In the fth study, Li et al. (2021) speci ed that there was a sharp drop in passenger air travel because of the COVID-19 for two reasons.These are the breakdown of demand and supply of restrictions.The study segmented passengers according to their characteristics by applying several simulations and predictions of demand for each segment.In the sixth study, Zhang et al. (2021) determined econometric and subjective models related to patterns of Hong Kong's tourism revival.These models described how the COVID-19 Pandemic affected Hong Kong's tourism industry economically.They also analyzed the airline revenues due to COVID-19 effect.In the seventh and last study, Xuan et al. (2021) forecasted the air transport recovery period.He used the vector autoregression approach to calculate the period of recovery.The results showed that the decisive factors of the recovery are gross domestic product (GDP) and air freight tra c.
The precautions for restricting the COVID-19 Pandemic spread have inhibitive in uences on the mobility of human beings globally.As a result of this circumstance, rst national and international air travel from and to China has been in a downward trend as of February 2020 (Iacus et al. 2020b).Then this downward trend has monitored globally.So, COVID-19 contaminations have negatively affected the large volumes of all transportation modules.These transportation modules connect to the increase in tourism for the economic level of countries (Iacus et al. 2020a).The tendency for SARS, MERS, and COVID-19 has globally spread more quickly than the increment of the world population in the last decade (Recchi et al. 2019).So, the ow of air tra c has been designated due to the national and international shocks because of political uncertainty, the crisis related to economic status of countries, and terrorism (Gabrielli et al. 2019).Furthermore, air transportation has indicated a signi cant dependence on the Pandemics in the former years such as 2003 SARS and 2015 MERS with in uences on the national and international scale.However, the level of COVID-19 Pandemic could not compare with these previous Pandemics (IATA, 2020e).
If such a Pandemic had not happened, there was a general supposition in the worldwide aviation industry to anticipate an increasing development trend in 2020.This status was the same as the consecutive growing years for air passenger and freight transportation.The forecast reports have shown this trend for airlines about the investments in buying new aircraft from widely known aircraft manufacturers such as Airbus and Boeing by directing new order deliveries.In addition to the manufacturing companies in civil aviation, the connection between the tourism and transportation sectors has broadly been debated academically.This debate is commonly focused on air transportation.Despite the existence of other modules in transportation such as railway, maritime, road vehicles, etc., tourism issue is the most decisive one for air transportation.Correspondingly, tourism is the preferential factor for the development of air transportation and the increment of GDP related to the economic level of countries (Khan et al. 2017;WTTC, 2017).
Civil aviation has turned into the most important one among the other industries in its contribution to worldwide economic development.However, the development and continuation of COVID-19 will cause economic issues related to excessive tourism costs on a global scale.Correspondingly, the implementation of measures is also about the operation process planning in a global eet of narrow and wide-body aircraft (IATA, 2020d).International tourism, which stands on air transportation with a ratio of (58%) for arriving passengers to countries, has reached a standstill with important ratios of negative outcomes for tourism-linked activities and numbers of employment (TandE, 2020).The necessity for the airlines related to stopping their ight operations has negatively affected the demand of passengers, so the airlines do not have enough options in the usage of airports for the sustainability of the ight planning strategy rather than to use aircraft for cargo ights.Besides, these selections are required to assist the airports and airlines by ensuring a particular eld for using new aircraft parking positions.The crisis in the civil aviation industry is related to interminable, connected, and unresolved problems designated for the worldwide air transportation framework (Browne et al. 2016).
When benchmarking air passenger and freight transportation, air freight is more complicated than passenger transportation because this transportation process includes more strategies and more detailed processes.When compare with passenger transportation, a compound of weight and volume, various types of services, combinations, and network planning design are more detailed.The obvious differences between freight and passenger operations demonstrate that the multidisciplinary nature of freight transportation is more complicated than passenger transportation (e.g., Bartodziej et al. 2009, Leung et al. 2009, Li et al. 2009, Wang and Kao, 2008).In general, air freight transportation has higher ambiguity than passenger transportation because of its volume capacity.In passenger transportation passengers may cancel bookings, so the passengers that do not come to the aircraft have no place on the passenger list.Because of this, International Civil Aviation Organization (ICAO) permits airlines for selling tickets at more than %10 of their capacity.The booking capacity of air freight transportation is related to the freight forwarders' planning and it can be assigned to the volume of cargo capacity.The cargo capacity volume plans the determined ights for six or twelve months (Amaruchkul et al. 2011).The planning of the number of goods shipped with on-time performance is more important rather than booked reservations.These reservations compose elevated uctuations due to the management of capacity.This situation shows freight forwarders generally do not require to give the price for unserviceable freights.Without punishment charges for unserviceable freights, the forwarder can ful l the need to reduce risks to compete with the other companies.This status actualizes with several reservations in air freight that have been planned, reserved, and cancelled after the plan because cancelled ights are not an expense for the airlines.Consequently, the reservation process can show substantial volatility in air freight more than air passenger transportation (Petersen, 2007).
It is more challenging to predict air freight capacity than air passenger capacity.Passenger aircraft capacity is related to its total seats, but freight capacity relies on the types and volume of containers and pallets named unit load devices (ULDs).The main problems with ULDs include variety of issues such as, pivot weight, volume, type of the product, and center of gravity (Leung et al. 2009).For example, capacity has a connection with volume, and solely weight is not a determining factor.The basic speci cations of air freight include complicated decision-making models for the management of air freight capacity.Transfer routes between the origin and destination (OD) pair are signi cant for air freight transportation.They serve the airline for passenger transportation.Generally, big-scale airlines known as full-service carriers control the process of alleged hub-and-spoke networks.Freight and passengers are carried from diversi ed origins to several hubs where freight and passengers are uni ed and afterward carry to other hubs for using wide-body aircraft.Passenger transportation can have a problem with inadmissible passengers.These passengers cannot embark to the aircraft due to the prohibitions.In air freight transportation, the freights can transfer via numerous midpoint airports such as origin point to destination point with a quick delivery time (Amaruchkul et al. 2011).
Airlines report the origin, stopover (transit), and destination airports for both passenger and freight tra c to build the transfer route plans.These processes cover network capacity usage and have a connection between conceptual and empirical modelling.These models have an increasing trend aiming to analyse quantitative decision methods related to the operational process especially for air freight (Feng et al. 2015).Furthermore, the literature review covers the information about air transportation with de ning the decreasing trend about all active countries because of COVID-19.Also, the literature review shows the decreasing and increasing trend of air transportation numbers by making a forecast (for passenger and freight) before and after the COVID-19 Pandemic.

Sample Of Data
For the 11 selected variables in this study, time series modeling was applied.The primary thing that affects air transportation statistics is gross domestic product (GDP).All nished products and services produced within the country for a particular time period (often one year) are included in the GDP (OECD Data, 2022).Additionally, the Federal Reserve Bank of St. Louis provided the GDP data (2022).The study's introduction and literature review sections both include descriptions of air passenger and freight transportation that indicate both the domestic and international numbers involved.The six airline variables that are still in effect are: available passenger kilometers (ASK), revenue passenger kilometers (RPK), passenger load factor for air passenger transportation (PLF), available tonne kilometers (ATK), revenue tonne kilometers (RTK), and cargo load factor (CLF) for air freight transportation.All selected variables are used for the time series modeling analysis between January 2016 and August 2022 due to the availability of data.
First, RPK and the airline's total kilometer passenger capacity are connected.The total number of seats own and the distance are added to determine RPK.RPK reimburses all miles own by paying passengers.The total distance traveled and the number of passengers who make revenue are multiplied to determine RPK.Because it assesses the current demand for air travel, sometimes known as airline "tra c." RPK determines the amount of demand for air travel with regard to the labor force or workforce by calculating the number of passengers and distance traveled (Revenue Passenger Kilometers, 2022).Secondly, ASK includes the available seat capacity of the aircraft, and it is a decisive data for the calculation of the airline's transporting passenger capacity.When a seat is available for carrying, it can calculate for the ASK (Available Seat Kilometers, 2022).Thirdly, PLF is the last widely accepted variable.
By dividing RPK by ASK, it is determined with the airline's capability for carrying passengers.The capacity of the passenger seats has an impact on the rate at which RPK and ASK are rising.It means PLF directly affects an increase in terms of ASK.So, PLF covers supply, demand, the total passenger numbers, and seat capacity (Passenger Load Factor, 2022).
Fourthly, ATK is related to the airline's total kilometer freight capacity.It is obtained by multiplying the distance by the total volume of capacity own.The number of available freights is signi cant for the evaluation of ATK and the calculation of the airline's transporting freight capacity.When a compartment is available for carrying, it can calculate for ATK (Available Tonne Kilometers, 2022).Fifthly, RTK covers the number of kilometers own by paid freights.It is de ned as the total distance traveled with the number of freights that generate revenue.It evaluates the actual demand for air travel as an airline's "capacity."RTK calculates the amount of labor or workpower used to measure the level of demand for air travel.RTK is multiplied by the distance travelled and the freight expense (Revenue Tonne Kilometers, 2022).LF is the nal extensively used variable.By dividing RTK by ATK, it is computed with the airline's capacity to move freight.RTK and ATK both rise in response to an expansion in this freight transport capacity.This indicates that CLF has a direct impact on an increase in ATK.So, CLF includes total freight capacity, total carriage volume, total supply, and total demand (Cargo Load Factor, 2022).
These factors re ect how well airlines are performing nancially and operationally.IATA has shared these six variables since January 2016, so the time period of the analysis start from January 2016 (IATA Air Passenger Monthly Analysis Reports, 2022; IATA Air Freight Monthly Analysis Reports, 2022).In this study, air passenger and freight transportation variables named RPK, ASK, PLF, ATK, RTK, and CLF analyzed in the time series modelling (Tsai and Kuo, 2004), and they obtained from the IATA Air Passenger Monthly Analysis Reports (2022) and Air Freight Monthly Analysis Reports (2022).Additionally, the air passenger and freight numbers took from the Bureau of Transportation Statistics (BTS) for Air Passenger Data (2022) and Air Freight Data (2022).

Methodology
As previously determined, this research uses IATA-released monthly data from January 2016 through August 2022.These factors are listed as follows: Gross Domestic Product (GDP), Domestic Passenger Numbers, International Passenger Numbers, Domestic Freight Numbers, International Freight Numbers, Available Seat Kilometer (ASK), Revenue Passenger Kilometer (RPK), Passenger Load Load Factor (PLF), Available Cargo Tonne Kilometers (ACTK), Revenue Tonne Kilometers (RTK), and Cargo Load Factor (CLF) (IATA Air Passenger Monthly Analysis Reports, 2020; IATA Air Freight Monthly Analysis Reports, 2020).This study includes time series modeling to forecast PLF and CLF while analyzing the contributing variables.Therefore, endogenous factors ASK, RPK, GDP, domestic, and international passenger numbers are considered in the Vector Error Correction Model (VECM), while endogenous variables CTK, ACTK, GDP, domestic, and international cargo numbers are thought to affect the CLF.After the VECM model has been applied, the relationship between PLF, CLF, and the other endogenous variables is made known to impulse response functions.In time series modeling, the series that are connected to the selected variables are transformed with a logarithmic transformation and normalized to remove variability by subtracting the mean and separating the standard deviation.To avoid NaN results caused by logarithmic transformations with negative values, plus 1 is added to all series.The time series analysis is carried out using the following packages: "TSA, vars, urca, forecast, and tsDyn" in R 4.0.2.(Pfaff, 2008).Understanding the stationarity and connection of the series can be accomplished by looking at the standardized series (Fig. 1 and Fig. 2).
In the period of January 2016 to August 2022, s_PLF, s_ASK, s_RPK, s_GDP, domestic, and international passenger number variables are shown in Fig. 1.It is obvious that a major drop is reported in April 2020 due to COVID-19 impact on all series.Although the increase in every variable has slightly started and continue after May 2020.s_RPK and s_ASK variables pass their previous level at the beginning of 2022.Besides, other series approximately reach their previous level (slightly lower) at the beginning of 2022 and pass their previous level at the third quarter (July and August) of 2022.
In the period of January 2016 to August 2022, s_CTK, s_ACTK, s_GDP, s_Domestic, s_International, s_CLF parameters are shown in Fig. 2. The COVID-19 Pandemic's impact is expected to result in a major drop in all data in April 2020, except for GDP.On May 1, 2020, the GDP will have increased and reached its peak value.In terms of s CLF, the series barely surpassed its prior level, but s_Domestic and s_International reached their top level in the third quarter (July to September) of 2022.

Unit root test and the lag-length determination
The idea of stationarity is very important in time series analysis.The covariance between two series values is expressed as the number of lags in the series, and a time series has a xed mean, variance, and stationarity.Once trend and seasonality modi cations have been made, time series models must be used (not changing over time).A subjective way of assessing stationarity is to use Augmented Dickey-Fuller (ADF) test statistics (Dickey and Fuller, 1979;Dickey and Fuller, 1981).The test is applied to a new model called the ADF test because the lags of the dependent series are expected to be added to the right of the equation to solve the autocorrelation problem.A test was suggested by Dickey et al. (1984)  In the formula, is K-dimensional vector of observed variables, is Kx1-dimensional constant vector, is a time trend, is the error term which has 0 mean and constant variance called white noise.Both the level of the series and their initial differences are tested in this procedure.In contrast to the alternative, the null hypothesis is that the series under examination has a unit root.In each example, the nal prediction error (FPE) from Akaike is minimized to determine the lag-length (1969).Additionally, the Likelihood Ratio Test (LR), Akaike Information Criteria (AIC), Schwarz Information Criteria (SC), and Hannan-Quinn Information Criteria (HQ) can de ne the optimum lag-length.In every test except the LR test, the smallest value indicates the ideal lag-length.By putting the likelihood ratio statistics to the test at the selected level of signi cance, the LR test is discovered.The proper lag-length should be long enough to prevent autocorrelation between error terms but short enough to prevent any loss of information regarding the interaction of the series (Kasapoğlu and Müdürlüğü, 2007).

The cointegration test
The cointegration test determines whether there is a long-term relationship between the series after the stationary study between the series.Three alternative approaches are utilized in the literature to incorporate the cointegration test into the model.These methods were improved by Engle and Granger (1987), Johansen and Juselius (1990), and Pesaran, Shin, and Smith (2001).Johansen and Juselius' (1990) technique was selected for this study because it allows for the examination of more than two variables.The absence of a cointegration vector in the series is the null hypothesis (H 0:r = 0).A different possibility for the cointegration vector (H 0:r0) is that the time series have one (cointegrated series I(r)).R is a symbol for the quantity of cointegration vectors.If there is at least one cointegrated vector in the study, it means there is a long-term relationship between the series in the model.In other words, the order of these series remains constant.The VECM ought to be incorporated into the model because it is determined whether a long-term relationship exists at this point in the investigation.

Vector error correction model (VECM)
Long-term and short-term relationships between series are separated by VECM.Engle and Granger (1987) created it to distinguish between short-term connections.It is attempted to assess whether the series experiences any shock over the long-term using VECM.According to Engle and Granger (1987), the operating model for the VECM is as follows: 2 In the formula, is K-dimensional vector of observed variables, is Kxr-dimensional coe cient matrix, is Kxr dimensional cointegration matrix, is kxk-dimensional short_term coe cient matrix, and is the error term which has 0 mean and constant variance called white noise.The error correction variable acts to maintain the model dynamics in equilibrium and compels the variables to converge on the Error Correction Term (ECT), which is the long-term equilibrium value.When the error correction term's coe cient is statistically signi cant, bias is present.The coe cient size is a measure of how quickly the value of the long-term equilibrium is approaching.In actual, it is anticipated that the error correction variable will be statistically signi cant and negative.The variables in this instance are said to move in the direction of the long-term equilibrium value.Short-term departures from equilibrium will be recti ed based on the size of the error correction variable's coe cient (Enders, 1995).The lag order is p.
The maximum lag and minimal Akaike Information Criteria are used to choose the lag-length p in the VECM.

Impulse response functions and the decomposition of forecast error variance
The estimated coe cients in VECM are quite challenging to comprehend.Impulse-response function (IRF) graphs, which are graphical representations of the reactions to varied shocks, are thus utilized to analyze the model's results.The vertical axis is used to generate the graphs of the impulse-response functions.The amplitude and direction of other series' responses indicate an increase in the standard deviation's response to the pertinent series.In a 12-month period, the shock is given a horizontal axis.Red-dashed lines re ect con dence intervals with 2 standard errors for how the variables will respond, and they are crucial in establishing the data' statistical signi cance.Indicating that the reaction is statistically signi cant at a 95% con dence level, the bottom and higher bands both had the same sign.
The dotted lines on the graphs show the con dence intervals, and the straight lines on the graphs re ect the point estimates of the effect-reaction coe cients.To verify the relationship between the series, the Forecast Error Variance Decomposition (FEVD) approach is used.A speci c variable's response to its own shock and the shock from other variables are evaluated in the VECM model, or FEVD.FEVD breaks down a variable's uctuation into its individual shocks.It simply divides the variance of each variable's forecast mistakes between its own shocks and those of the other variables in the VECM (Omisakin, 2008).

Forecasting
Recursively, forecasts are made for the series' levels.By converting VECM to a VAR in R (using the VARrep function), forecasts for VECM can be obtained.Since a VECM with a lag of p corresponds to a VAR with a lag of p + 1, the new data for a VECM with a lag of p should have p + 1 rows.

Results
ADF test results for evaluating stationarity, cointegration test results, estimated VECM model results (for s PLF), s PLF impulse response, forecast error variance decomposition, forecasting of s PLF, and forecast values for passenger load factor are shown in the results section with tables and gures.

Unit root test and determining delay
The unit root of the series the null hypothesis.The time series being stationary is an alternate theory (or trend-stationary).As shown in Table 2, the number of s_ASK, s_GDP, s_Domestic, and s_ International variables all reject the null hypothesis at the 0.05 signi cant level.The initial difference between s_PLF and s_RPK is discovered stationary.As shown in Table 1, the null hypothesis is rejected at the 0.05 signi cance level.The AIC, HQ, SC, and FPE tests are taken into account to estimate lag-length.The structure of VECM model is used in these tests to establish the ideal lag-length for this data set, which is 10.Despite the small sample size and the series' structure, the lag-length is set at 2. So, in order to forecast s_ PLF and s_CLF, the cointegration test is required.It can be utilized with the series in the estimate of regressions.

The test of cointegration
r indicates the equations number.The test statistic is low for r = 1 for s_PLF and r = 3 for s_CLF models at 5% signi cance level, rejecting the hypothesis.Table 2 shows the cointegration's presence that VECM was used to nd the result.The acquired results led to the formation of a VECM with r = 1 and r = 3 cointegration vectors.As previously indicated, the model's lag length is assumed to be 2.In Table 3, the estimated VECM results are shown.The Error Correction Term (ECT) controls how quickly long-run equilibrium returns.ECT1 > 0, ECT2 > 0, and ECT3 > 0, or at least one of them cannot be equal to 0, are necessary for a long-term connection to be stable.Table 3 shows that it does meet the prerequisite for a long-term stable connection.The error correction model will re-establish s_PLF's and s_CLF's long-term equilibrium because it is statistically signi cant and negative.Approximately 18% (s_PLF) and 30% (s_CLF) of the variances are corrected when there is a departure from equilibrium.The impulse-response functions are discussed in the next part to further explore the long-term impacts.

Impulse response function
For the results to be regarded as valid, both IRF con dence intervals must remain in the area above (or below) the zero band.As a result, conclusions from the research may only be drawn if the con dence intervals fall within the same range.
The top graph, in the middle of the left side, demonstrates that s_PLF started to fall after being temporarily touched by the effect, and then the effect disappears.According to the bottom-left graph, the short-term in uence of s_Domestic_c on s_PLF increased, while the long-term effect of this impact gradually declined.The bottom right-hand graph demonstrates that after being touched by s_ International, s_PLF started to rise, and this impact gradually subsided in long-term.The bottom graph in the middle left-hand column demonstrates that s_CLF started to rise after being negatively affected by itself for a while, and eventually the effect disappears.The bottom right-hand graph demonstrates that the short-term in uence of s_International_c on s_CLF was followed by an increase before the impact disappeared.The graph on the bottom left shows that s_CLF started to increase after being temporarily touched by s_Domestic_c, and subsequently this impact disappears.After being affected by s_ GDP in the near term, s_CLF started to rise, and this impact gradually lessened in long-term (Fig. 3).

Decomposition of forecasting error variance
By dividing the variance of forecast error, it is possible to observe the impact of independent variables on s_PLF and s_CLF.The variance decomposition of forecast error examines the relative contributions of various variables and shocks to changes in a series.To nd the impact of other series on a shock that happens in any of the series, variance decomposition is used.It de nes the percentage of a shock unit that happened in one series that was brought on by changes in another.
Figure 4 shows the FEVD results, which indicate that depending on how the series is coupled to the shock, the key variable in uencing the s_PLF can alternate between the s_GDP, s_Domestic, and s_International.
The primary factor in uencing the s_CLF can either be s_International_c, s_GDP, or s_ CLF by itself depending on how the speci c series is tied to the shock.

Forecasting
The VECM produces projected outcomes for the next nine months.Long-term results will be more accurate when the model is expanded to include the s_PLF and s_CLF values for each month.The ndings of the forecast are as follows.
In Fig. 5, the red lines show the upper and lower boundaries, while the blue line show the conditional forecast.The s_PLF series are somewhat decreased after August whereas the s_CLF series are signi cantly raised after August that seen in the forecasting results in Fig. 5.The predicted outcomes can be analyzed because model assumptions are revealed.With the VECM, the nine months forecasting can be applied to the analysis.Table 4 also includes the real data from December for comparison's sake.Due to the fall and winter seasons, it is anticipated that the slightly negative trend for s_PLF will persist for the next nine months.Therefore, the impact of the rst and fourth quarters (October to December and January to March) stands a very low level.It is forecasted that the slightly upward trend will proceed in the following three months and slightly decreased in the other 6 months for s_CLF according to the potential of economic crisis in the rst quarter (January to March) of 2023.

Conclusion
COVID-19 effect is negatively differentiated from all Pandemics and also crises due to its dissemination globally.Due to its nature, air transportation is the industry that mostly effected from crises and Pandemics globally.Air transportation includes air passenger and freight transportation, and they have different characteristics from each other.In general, air freight is more sophisticated than air passenger transportation because it includes more complicated processes.The calculation weight and volume, diversi ed services, combination, and reinforcement of network planning include more diversi ed speci cations than passenger transportation.The signi cant distinctions between passenger and freight operations reveals that freight transportation have a more multidisciplinary system and higher uncertainty than passenger transportation due to the capacity problem related to volume.However, in passenger transportation passengers may cancel bookings, so the passengers that do not come to the aircraft have no place on the passenger list.Forecasting air freight capacity is also more complicated than forecasting air passenger capacity.Passenger aircraft capacity is related to total seat number in the aircraft, but freight capacity relies on the types, volume of containers pallets named ULDs.Besides the differences between two modules of transportation, gross domestic product (GDP), total national air passenger numbers, total international air passenger numbers, total national air freight numbers, total international air freight numbers, available seat kilometer, revenue passenger kilometer, passenger load factor, available cargo tonne kilometer, revenue cargo tonne kilometer, and cargo load factor are the selected parameters for the application of time series modelling.
In the methodology part related to the analysis of air passenger transportation between January 2016 and August 2022, s_PLF, s_ASK, and s_RPK variables dramatically decrease in April 2020 because of the COVID-19 Pandemic except s_GDP variable.Even if the increase has gradually begun and will continue to rise beyond May 2020, the series has not yet returned to its prior level (slightly lower).In the methodology part for air freight transportation between January 2016 and August 2022, s_CTK, s_ACTK, s_GDP, s_Domestic, s_International, s_CLF variables dramaticly decrease in April 2020 because of the COVID-19 Pandemic except s_GDP variable.The series returns to its former level for s_CLF, s_Domestic, and s_International with the rise trend in GDP on May 2020, although s_ GDP value has peaked.In the forecasting of a 9-month period using VECM, it is predicted that the slightly downward trend for s_PLF in air passenger transportation will continue in the coming 9 months due to weather conditions in the fourth and rst quarters, whereas the slightly upward trend for s_CLF in air freight transportation will continue in the coming 3 months and slightly decrease in the remaining 6 months due to the potential economic problems globally in the rst quarter.In future studies, a different analysis named Multidimensional Scaling can be applied with the same variables for all active countries in civil aviation on yearly basis.

Declarations
Author has no personal interests from other parties.

Ethical Approval
Ethical approval is not needed due to open source resources.
Domestic Product (GDP), Total National Air Passenger Numbers, Total International Air Passenger Numbers, Total National Air Freight Numbers.Total International Air Freight Numbers Available Seat Kilometer for Air Passenger Transportation Revenue per Passenger Kilometer for Air Passenger Transportation Passenger Load Factor for Air Passenger Transportation Total Available Cargo Tonne Kilometer for Air Freight Transportation Revenue per Cargo Tonne Kilometer for Air Freight Transportation Cargo Load Factor for Air Freight Transportation related to issues in autoregressive time series.Here is how this test is shown.

Table 1
ADF test results to show the evoluation of stationary

Table 4
The forecasting values of passenger and cargo load factor