A new modelling approach for air transportation A case study for total number of air passengers per

Abstract

Keywords: Modelling Air Passengers; Studentized Residuals; Correcting Heteroscedasticity; Studentized RCEV Test; Weighted Regression; Forecasting

Introduction

Air transportation has been a driving power of economic and social development [1–3]. Furthermore, the growth of the aviation industry enhances the trade development in a country, in turn; it provides a great deal of contributions to its wealth [4]. However, unqualified employees,

inadequate ground operations, and political and economic conflicts have negative effects on civil aviation. In addition, poor service quality [5], trade barriers [6], ticket prices [7], competition with high-speed trains [8], market shocks and terrorist attacks [4] or pandemics -like Covid-19- create undesired impacts on air transportation industry. The

*Corresponding author. *E-mail address: h.aykut.karaboga@amasya.edu.tr This paper was recommended for publication in revised form by Regional Editor-in-Chief Ahmet Selim Dalkılıç Published by Yıldız Technical University Press, İstanbul, Türkiye Copyright 2021, Yıldız Technical University. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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COVID-19 pandemic has had a significant impact on air passenger demand, causing a sharp decline in the number of air traveling demands. Despite the pandemic, air passenger demand is expected to grow steadily in the long term due to factors such as rising disposable incomes, the growth of international trade, and the increasing popularity of air travel among the middle class. In conclusion, air passenger demand is a critical aspect of the aviation industry, driving growth and development but also presenting significant challenges that must be addressed. As the world emerges from the pandemic and the aviation industry adapts to the new normal, it will be essential to balance growth with sustainability and address the economic and social impacts of air travel. Thus, accurate demand forecasting models could minimize the mentioned social, economic, and political effects. Demand forecasts reduce stakeholders’ risks and create accurate transportation systems [9]. Demand forecasting is critical in airport operations to manage immediate operational reflections [10,11]. The consequence of operating inaccurate forecast models falls into several factors such as capacity optimization faults, increased operation costs, airport accumulation, and customer dissatisfaction. In this regard, managers, policy makers, and airport planners should be able to use a simple and efficient forecasting model to take necessary precautions. Long-term and shortterm strategic transportation plans [12] -with accurate forecasting models- play a primary role in the air transport market, where volatility and risk are high. Some discussions about demand forecasting can be seen in Hakim & Merkert [9], Wang & Song [13] and Wang & Gao [14]. Moreover, for macro (overall sales projections for strategic planning) or micro level (day to day or hour to hour) planning approaches and analysing methods we recommend to the readers detailed review [15]. In this study, we create a robust forecasting model for the demand of air the number of passengers, using a weighted regression model that has never been cited in the air transportation studies. To sum up, our major research questions are: • Can we provide a simple and efficient model for policy makers and airport planners? • Is our model providing linear regression assumptions? • Does a Weighted Regression model show a satisfying forecasting performance for the demand for the total number of air passengers per month? The parts of the study are as follows: In the section 2, brief literature on air passenger demand forecasting was introduced. In the section 3, methodological approach used in the study was clarified. The data were presented data in the section 3. As for the section 4, analysis, results, and forecast results were presented. The final section is devoted to the evaluation of the research results, conclusions, and future research suggestions.

Literature Review

The studies about the air passengers’ demand of generally focus on developed countries and especially due to their aviation history on the United States and the United Kingdom. Asia and in Africa focused studies provide insight on developing industries as well [16]. Thus, the developments in this field can be easily examined. In the literature review, demand modeling approaches are generally categorized under three different headings: time series based, artificial intelligence-based, and linear regression-based approaches. Regarding time series-based approach; Pitfield [17] modelled air passengers of United Kingdom with autoregressive integrated moving average (ARIMA). Bermúdez et al. [12] forecasted United Kingdom monthly air passenger data with additive Holt–Winters and maximum likelihood methods. Since the usage of the Holt–Winters forecasts inappropriate with sessional data, they transformed stochastic part of the data and the model provided homoscedastic, uncorrelated, and multivariate normal distributed residuals. Gelhausen et al. [18], forecasted German air passenger demand with co-integration theory-based model and compared with the classical four-step forecasting model. Additionally, they supported model success with the Brexit effect on traffic volume for German airports. Karlaftis [19] used the dynamic TOBIT model to estimate the monthly number of passengers of Corfu airport. In this study, Karlaftis underlined the accurate modelling for airports with high seasonal volatility. Considering the hybrid artificial intelligence approach, Ming et al. [20] built a Hybrid ARIMA-SVMs model to predict multistep-ahead air transportation demand. However, the overtraining of the Support Vector Machine (SVM) got worsened the predictive performance of the hybrid ARIMASVM model. Carson et al. [21] compared aggregate and disaggregate air travel demand forecasts with quasi-aggregating individual markets (quasi-AIM) approach and forecasted monthly US civil aviation data. But data showed heterogeneity so, their disaggregate model outperformed to other models. According to Xiao et al. [22] decomposed data into three parts: seasonal, trend and irregular components. The model is composed of three parts too: generalized regression neural network (GRNN), singular spectrum analysis (SSA), and radial basis function networks (RNFNs). Their ensemble model overachieved in forecasting HKIA air passengers. Xiong et al. proposed an integrated approach using the MI-SVR machine learning model to predict air passenger traffic at Shanghai Pudong International Airport. The model incorporates key influencing factors based on mutual information, resulting in improved prediction accuracy compared to conventional methods [23]. Tang et al. developed a model to forecast short-term daily passenger traffic at a major airport terminal in China during the COVID-19 pandemic, which reduces model error by 27.7% compared to a baseline model and provides implications

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for airport operations [24]. In their study, Jin et al. (2020) evaluate various forecasting techniques, including ARIMA, ARMA, and machine learning, and propose that a hybrid approach using variational mode decomposition (VMD), ARMA, and kernel extreme learning machine (KELM) provides the most accurate predictions for future passenger traffic at three major Chinese airports [25]. Regarding linear regression-based forecasting, Abed et al. [26] used stepwise regression method in order to modeling Saudi Arabia’s international air passengers demand. They tried to prevent multicollinearity, and they examined the variable relationships with 4 different models. It was revealed that total expenditures and the population were the most important variables that affect international flight demand in the country. Aderamo [27] analysed effecting factors of Nigerian domestic air transport demand with multiple linear regression method. He underlined that governmental support to improve air transportation systems in developing countries. Baikgaki [28] obtained a linear regression model for Republic of South Africa’s domestic air passengers demand. They used stepwise regression to solve the multicollinearity problem. Sivrikaya and Tunç [29] forecasted domestic air passenger demand of Turkey for city pairs with a semi-logarithmic regression model. The adjusted R squared score of the model was 86.4%. The authors emphasized the potential of air travel demand forecasting for a new airport. Hakim and Merkert investigated the factors influencing air transport demand in South Asian nations between 1973 and 2015 using fixed-effects models and a three-step error correction model [9]. Naghawi et al. developed an econometric air passenger demand model in Jordan with 6 demand determinants using stepwise regression and multiple linear regression analysis with annual data from 2006 to 2017 [30]. In the literature review, we realized that air passenger data are irregular, high volatile and seasonal [31]. As stated Karlaftis [19], correct and unbiased forecast models become more significant in touristic regions like Antalya, İzmir or İstanbul. Air traffic or demand forecasting with daily and weekly data is more troublesome compared to monthly data as well [17]. However, the demand of forecasting the seasonal, auto-correlated, and non-stationary data is troublesome for artificial intelligence-based or econometric-based approaches. But adding seasonal dummies to model improve forecasts [32], and simple models give better results compared to complex models and external factors [33,34]. In the literature review, we have not found any similar application with Weighting Absolute Centered External Variable Method (WCEV) [35] forecast the demand of air the number of passengers, except WCEV method was successfully applied International airline passengers-(monthly total from jan 1948 to dec 1960) in [35] (data is available at https://www.kaggle.com/datasets/andreazzini/international-airline-passengers). The study does not contain forecasting. As a different approach to modeling air passenger

demand, this study contains a forecasting model in which the months are independent variables and the total number of air passengers per month is dependent variable. Additionally, we eliminated the external factors and seasonality with a trend variable. Normality assumption is checked with the histogram of Studentized residual and homoscedasticity assumption is checked with studentized residuals plots [36] and studentized RCEV test [37].

Materials And Methods

Data Description The contributions supplied by the state to the aviation industry have provided strong growth in the aviation industry in recent years in Turkey. Turkish air transportation industry has still been developing greatly [38]. The development of the last fifteen years is a result of the liberalization of the markets. In this context, geographical position, growth potential and touristic attraction provide momentum to Turkey with its technological support, such that purchasing tickets, booking and check-in can be easily carried out from the websites of companies or other e-commerce websites. For example, liberalization in Turkish Civil Aviation has been a driving force in industry growth with its annual average 10% since 2003 [29]. The General Directorate of Turkish State Airports Administration (TSAA) has been serving the civil aviation of Turkey since 1933. After the year 2003, when domestic flights opened to competition of private airways, there has been an enormous increase in the total numbers of passengers, flights, number of destinations, and operating companies. The total number of destinations in 2014 was 53 from 7 centers with 6 airway companies for domestic flights and 237 from 108 countries for international flights. TSAA forecasted the total number of passengers 238 million for 2020 and 247 million for 2021, including direct transit passengers. Therefore, we should create accurate and simple models in order to manage air transportation potential. We obtained the data from the monthly reports of TSAA.

Methods

Regression analysis is well-known method in the statistics. Normality, homoscedasticity, uncorrelated residuals, and independent variables are the basic assumptions in classic linear regression analysis [39,40]. Homoscedasticity is one of the classical linear regression analysis assumptions. The homoscedasticity assumption is a central assumption of linear regression theory [41]. The distribution theory and statistical inference based on confidence intervals and tests of hypotheses are valid and meaningful only if the standard linear regression assumptions are satisfied [35]. Therefore, checking the homoscedasticity assumption is vital in linear regression analysis. In this study we checked normality of residuals and outliers with the histogram of the studentized residuals;

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homoscedasticity is checked with studentized RCEV test and scatter plots of studentized residuals vs months (as stated by Bischof et al. [42], if model specified correctly, studentized residuals are homoscedastic). The model sufficiency is evaluated with the F test, adjusted R2, and standard errors. For extended information and application codes we encourage readers to Çelik’s studentized RCEV test development study [37] and WCEV studies [35,36]. Some simulation of applications of the WCEV and Studentized RCEV test can be seen in Çelik [36,37] respectively.

of the variance and absolute residuals can be thought of estimating relative standard deviations. Squared residuals can also be used in this step. The first-order derivative of this function with respect to the external variable d is

Method

WCEV algorithm [35,36] that corrects heteroscedasticity is given below. For the regression model given in equation 1, (1) Ordinary least squares (OLS) parameter estimates, fit , values, and residuals are obtained by and respectively. Data is sorted by fitted values ascending order (In time series data is sorted by months ascending order). The external variable d is in sorted data, where d demonstrated as denotes the external variable and n denotes the sample size. The regressing external variable on absolute residuals or is given below (2) Where denotes standard deviation of estimates and α1, α2 are parameters to be estimated. As stated in Carroll and Ruppert [43] squared residuals can be thought of as estimates

(3) The point that makes the derivative function equal to zero is the widest vertically part of the BDR surface. This point is called the nodal point of absolute residuals. Nodal point is obtained by setting the derivative equal to zero and solving for d: (4) where is the nodal point estimation (dotted line in Figure 1-a and 1-b). The transformed centred external variable with respect to nodal point is given in equation 5. (5) where oi denotes centred external variable. The weight estimations are obtained by taking absolute values of the centred external variable as in equation 6. (6) where denotes weight estimation, |oi| denotes the absolute value of oi and γ denotes a scalar that maximizes log likelihood functions is given in equation 7 along a grid of values in a range of interest under the normality assumption. (7)

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Where, MSEw denotes the mean square error as in equation 9, n denotes sample size, and k is the number of parameters to be estimated. Finally weighted least squares are performed as in equation 8.

Now the interest is whether slope of Equation 15 γ = residuals are 0 or not. If γ = 0, homoscedastic, otherwise residuals are heteroscedastic. Hypotheses:

Homoscedasticity Heteroscedasticity Significance of γ is tested by the t-test by: (16)

(10) As Stated by Son and Kim [44], WCEV is superior to other robust estimation methods because WCEV provides the less auto-correlated residuals, smaller CV and RMSE than other traditional estimation methods. Since WCEV does not violate regression assumptions and is applicable to data with various heteroscedasticity types, WCEV can be practically used in correcting heteroscedasticity problems. In particular, WCEV provides more robust estimations when the variance of residual is a function of explanatory variable whose grid values are not smooth. Figure 1 shows how the WCEV method works.

or homosceFor dasticity assumption is valid and α/2 homoscedasticity assumption is valid. The flow diagram of the application is given below:

RCEV Heteroscedasticity Test Based on the Studentized Residuals (Studentized RCEV) Test The studentized residuals have a mean value of 0 and a variance of 1 [45]. For the regression model in equation 1 OLS parameter estimates, fit values, raw residuals and are obtained by matrix form follows as: (11) (12) (13) The vector of the studentized residuals r is obtained by the follow equation: (14) where

where k denotes the number of parameters to be estimates and n denotes the number of observations in the model. After obtaining studentized residuals, then RCEV studentized test is performed for auxiliary regression: (15) where a denotes intercept, γ denotes the slope parameter (Figure 1-c), and |oi| denotes absolute transformed centered external variable as in equation 5.

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Our study contains a forecasting model in which the months are independent variables with a trend variable and the total number of air passengers per month is the dependent variable. We also used a linear regression model to forecast monthly total passengers from February 2017 to December 2018. Specifically, the approach recently proposed by Çelik [35] to solve heteroscedasticity problem in linear regression models and to obtain a robust model.

the reference month. The variations in the accumulated number of passengers per-month are significant, except for November, which that means the mobility of number of air passengers are the same in November and December in Turkey. From the histogram of Figure 4 (left side), it can be concluded that, OLS provides the normality of the residuals. According to the studentized RCEV test of the OLS model in Table 1, and scatter plot of the residuals against month (Figure3 right side) homoscedasticity assumption is violated. Scatter plots of studentized residuals vs months indicates butterfly distributed residuals pattern, which is a particular type of heteroscedasticity. Graphical analysis of the residuals demonstrates that the normality assumption is provided (Figure 4). According to the studentized RCEV test, it was found that the homoscedasticity assumption was ensured and the butterfly distributed residuals problem is eliminated. Also, the distribution of residuals indicates that the weighted model’s residual distribution is closer to the normal distribution compared to OLS residuals. Monthly and yearly increases demonstrate that the weighted model can be more efficient and so, forecasting results can be more accurate.

Results And Discussion

In this study, at the first step, we built an Ordinary Least Squares (OLS) regression model. Since regression assumptions are not provided, the WCEV weighting method is applied. According to the model used in this study, independent variables refer to months (X) and dependent variable (Y) refers to total monthly air passengers. The equation is given in (17). (17) Figure 3 represents the variation in the total monthly number air of passengers of Turkey from January 2007 to December 2018. The total numbers of passengers increased year by year. When we examined the data, we realized that the number of air passengers demanding flight seemed to be accelerated in the months of October, November, and December. Parameter estimations and statistics of OLS and WCEV are given in Table 1. In our model, we avoided a dummy variable trap by selecting December as the reference month. For this reason, β coefficient of the November is not significant with respect to the reference month. The coefficient of the other variables and trends are significant. The adjusted R2 of the model was 92.01%. The significance of the dummy variables was evaluated according to

Forecasting Results Demand forecasting is a major topic for strategic planning and policy making [15]. A lot of paper modeled air transport demand based on demographic factors, socio-economic and competition factors [14]. Differently, our study focuses on the data of passengers who are demanding flights monthly. Thus, other variables are shown with the trend and error variables in the model. Additionally, all air passenger data analyzed instead of a single airport data. In this way, it is aimed to formulate the general lines of aviation policies more easily.

Figure 3. Total monthly passengers according to months of years

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Table 1. Regression analyses results of OLS and WCEW The OLS Regression Model Variables

Results

Analysis of Variance Results: F=122.93<0.000. Significance: *p<0.10, **p<0.05, ***p<0.001.

Figure 4. Histogram plot and studentized residuals and scatter plot of studentized residual vs. months of OLS.

Figure 5. Histogram plot and studentized residuals and scatter plot of studentized residual vs months of the WCEV.

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Figure 6. Forecast results of the EWMA models for comparison with WCEV.

Significance: * p<0.10 ** p<0.05 *** p<0.001. MAD: Mean Absolute Deviation; RMSE: Root Mean Squared Error.

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In this section, the WCEV and EWMA methods in the weighted estimation methods are compared. The EWMA method is a control procedure, and it is highly effective in detecting systemic changes in continuous variable processes. The method makes a continuously updated prediction by assigning a certain weight to the current observation values and previous observation values [46]. The method reduces the impact of previously observed data while placing more emphasis on the most recent observations. This makes it faster and more accurate in detecting systemic changes in the process. The EWMA method is particularly useful in many areas of industrial applications, such as quality control and process control. Compared to other control chart methods where the previous observation values are associated only with the latest value, the EWMA method is more precise and faster. Therefore, the EWMA method is a valuable tool for monitoring and controlling continuous variable processes in industrial applications [47]. Figure 6 displays the compatibility between the forecasted values and the real values. The forecasted values are obtained using 3 and 4 lag EWMA models with the WCEV method. As evident from the graph, the forecasting results obtained using the WCEV method is closer to the real values. Further detailed comparison results can be found in Table 2. As Stated by Son and Kim [44], WCEV is superior to other robust forecasting methods because WCEV provides the less auto-correlated residuals, smaller CV and RMSE than other traditional estimation methods. When the values in the table are examined, it can be observed that the WCEV method provides forecasts with a higher confidence level. The RMSE and MAD values also indicate a lower deviation compared to the EWMA methods. Mean for real values and forecasts are 103.635 and 97.945; standard deviations are 62.286 and 97.945 respectively. The correlation with real and forecast values is very high (0.996). The mean difference of real and forecasted values is not significant as well. Also, the mean absolute deviation and root mean squared error values are smaller than EWMA (3) and EWMA (4). Although, data is highly volatile, successful forecast results are obtained.

interpret the coefficients of the variables in the obtained models. Instead, it would be beneficial to use more practical, understandable, and simple models. The WCEV method is one of these simple methods, which is a weighted regression model. This study provides a detailed description of the steps followed to develop a weighted econometric model of air travel demand in Turkey. The model analyses the number of air passengers as a function of months try forecasting the number of air passengers by establishing a statistical relationship between the air passengers and months. To compare the models, whether the model obtained satisfies the statistical criteria were evaluated with the RCEV test and graphically. The model obtained by the WCEV method is excellent in terms of goodness-of-fit criteria; there is no heteroscedasticity and multicollinearity problem. Weighting according to months in the model ensured that the model produces more accurate forecast results than the EWMA methods and all regression assumptions provided. It has been understood that the results are more robust and reveal narrower confidence intervals. One of the prominent findings of the study is that the passenger mobility increases at the last quarter of each year for Turkey. Furthermore, Turkey’s total monthly number of passengers is the lowest in January and February. When this information is taken into account, the necessity of weighting is revealed. As a result, the WCEV method produced better results compared to the classical OLS model. The second finding of the study is that January or February can be the best time period for the heavy maintenance of airports and airplanes with the lowest air passenger demand in Turkey. Therefore, it is possible to attract quality-sensitive or price-sensitive passengers with developing competitiveness based on technological, operational, engineering, and services capabilities that are based on flight security will be based on this productive time assessment. In conclusion, the capacity for runway, number of planes, and total service personal can be increased in peak months. Finally, the forecasting results show that the growth of the sector will continue due to the growth in the country. We predict a significant increase in the number of passengers thanks to the construction of new airports, cheap ticket prices, and low-cost carriers. In further studies, we are planning to analyse effect of the increase in air passenger demand and unqualified human resources on the firms’ operations and performance. Because we believe all these conditions should be taken into consideration to eliminate the economic loss.

Conclusion

Given all applications of new techniques for modeling research in the air transportation industry, the smallest improvements can provide a great competitive advantage among players. In this industry, where even the smallest costs are calculated, any contribution is welcomed to reach more accurate demand forecasts. Furthermore, in areas with high investment costs, especially in the aviation sector, modeling errors may cause great economic losses. However, we observed that the simplest, most accurate, and useful models are preferable. Recently, hybrid and weighted methods have been commonly preferred. However, hybrid methods generally complicate the modeling of the process and make it difficult to

Data Availability

All datasets are available at the General Directorate of the Turkish State Airports Administration (TSAA) statistics website.

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Data Availability Statement

The authors confirm that the data that supports the findings of this study are available within the article. Raw data that support the finding of this study are available from the corresponding author, upon reasonable request.

Conflict Of Interest

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Ethics

There are no ethical issues with the publication of this manuscript.

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