Forecasting Air Traffic Volumes Using Smoothing Techniques JOURNAL OF AERONAUTICS AND SPACE TECHNOLOGIES JANUARY 2014 VOLUME 7 NUMBER 1 (65-85) FORECASTING AIR TRAFFIC VOLUMES USING SMOOTHING TECHNIQUES Emrah ÖNDER* Sultan KUZU Istanbul University , School of Business, Quantitative Techniques Department, Istanbul, Turkey [email protected] Istanbul University , School of Business, Quantitative Techniques Department, Istanbul, Turkey [email protected] Received:,22nd October 2013 Accepted: 16th January 2014 ABSTRACT For many years, researchers have been using statistical tools to estimate parameters of macroeconomic models. Forecasting plays a major role in logistic planning and it is an essential analytical tool in countries’ air traffic strategies. In recent years, researchers are developing new techniques for estimation. In particular, this research focuses on the application of smoothing techniques and estimation of air traffic volume. In this study four air traffic indicators including total passenger traffic, total cargo traffic, total flight traffic and commercial flight traffic were used for forecasting. Also seasonal effects of these parameters were investigated. As analysis tools, classical time series forecasting methods such as moving averages, exponential smoothing, Brown's single parameter linear exponential smoothing, Brown’s second-order exponential smoothing, Holt's two parameter linear exponential smoothing and decomposition methods applied to air traffic volume data between January 2007 and May 2013. The study focuses mainly on the applicability of Traditional Time Series Analysis (Smoothing & Decomposition Techniques). To facilitate the presentation, an empirical example is developed to forecast Turkey’s four important air traffic parameters. Time Series statistical theory and methods are used to select an adequate technique, based on residual analysis. Keywords: Air Traffic Volume, Forecasting, Smoothing, Decomposition, Time Series, Turkey. HAVA TRAFİK YOĞUNLUĞUNUN DÜZGÜNLEŞTİRME YÖNTEMLERİ İLE TAHMİNİ ÖZET Uzun yıllardır araştırmacılar makroekonomik modellere ait parametrelerin tahmininde istatistik araçlar kullanırlar. Tahminleme lojistik planlamada önemli bir yere sahiptir ve ülkelerin hava trafik stratejilerinin belirlenmesinde kullanılan bir sayısal yöntemdir. Bu araştırmada özellikle düzgünleştirme tekniklerinin uygulanabilirliği ve hava trafik yoğunluğunun tahminlenmesine odaklanılmıştır. Çalışma kapsamında toplam yolcu trafiği, toplam kargo trafiği, toplam uçak trafiği ve toplam ticari uçak trafiği olmak üzere dört hava trafik yoğunluğu parametresi incelenmiştir. Bunun yanı sıra bu parametrelere ait mevsimsel etkiler tespit edilmiştir. İstatistik analiz araçları olarak hareketli ortalamalar, üstel düzgünleştirme, Brown’ın tek parametreli doğrusal üstel düzgünleştirme yöntemi, Brown’ın ikinci derece üstel düzgünleştirme yöntemi, Holt’un iki parametreli doğrusal üstel düzgünleştirme yöntemi ve zaman serilerinin bileşenlere ayırma yöntemleri gibi klasik zaman serisi yöntemleri Ocak 2007-Mayıs 2013 döneminde gerçeklesen hava trafik yoğunluğu üzerinde uygulanmıştır. Araştırmada klasik zaman serisi yöntemlerinin (Düzgünleştirme ve Ayrıştırma) uygulanabilirliği üzerinde durulmuştur. Uygulamada Türkiye hava trafik yoğunluğuna ait dört parametre kullanılmıştır. Zaman serisi istatistiki altyapısı, metotları ve hata ortalamasından yararlanılarak uygun tekniğin seçimini sağlamıştır. Anahtar Kelimeler: Hava Trafik Yoğunluğu, Tahminleme, Düzgünleştirme, Zaman Serileri, Türkiye. ______________ * Corresponding Author ÖNDER, KUZU 65 Forecasting Air Traffic Volumes Using Smoothing Techniques 1. INTRODUCTION Forecasting is the center tool of the planning and control processes. The objective of forecasting is to provide information that can be used to evaluate and clarify the effects of uncertainty about the future. Thus, financial planning and resource allocation can be done successfully. The logistics services industry will be significantly affected by future developments throughout the world [1]. It is estimated that this century will be dominated by air transport, both for domestic and international carriage of passengers and freight [2]. Air transport is an important part of logistic sector. Therefore, developing statistical analysis and forecasting tools are key elements for long-term strategy development and decision support systems for logistic decision makers. But there are not sufficient logistics researches about air traffic forecasting. In this paper, we apply forecasting techniques to the air traffic data for the future of the air logistics services industry till the year 2023. The strategic decisions of airlines involve analysis such as air traffic forecasting, the cycles of orders and deliveries, airline design [3], production planning, research and development, profit cycles, airline growth and survivability [4]. Although there are not many air traffic forecasting researches in literature, some of the studies are shown below. Adrangi, et al. (2001) examines the behavior of the US airline industry’s service demand using GARCH models [5]. Jonga et al. (2004) develop meta-model includes forecasting and simulation for passenger and freight transport in Europe [6]. Matsumoto’s research (2004) examines international urban systems from the standpoint of international air traffic flows and analyzes the patterns of international air passenger and cargo flows within and among the Asian, European and American regions from 1982 to 1998 [7]. This paper’s results reveal that Tokyo, Hong Kong and Singapore in Asia, London, Paris, Frankfurt and Amsterdam in Europe and New York and Miami in the US are strengthening their positions as international hubs. Lee (2009) proposed a modified social network analysis model for use in the examination of the international air network by estimating connectivity of the air routes, using the air traffic and the number of air routes [8]. With analyzing 1992-2004 data, it was observed that London, Paris, Frankfurt, Amsterdam, and New York were first class cities that were at the top in both years. Hui et al. (2004) provides an analysis of China’s air cargo flows identifies major air transport hubs in China and examines cargo movements between them [9]. Their paper shows overall statistics on China’s aviation and describes air cargo trends in China. Hwang and Shiao (2011) develop a gravity model of air cargo flows based on the panel data of air cargo services on scheduled routes at Taiwan Taoyuan International Airport during the years 2004–2007 [10]. Their results indicate that population, air freight rate and three dummy variables, including the regional economic bloc of the ‘‘Chinese Circle”(an informal partnership between Hong Kong, Macao, Taiwan and mainland China), the Open Sky Agreements and long established colonial links, are key determinants of international air cargo flows from/to Taiwan. Mason (2005) addresses the inexorable decline in yield in the airline industry regarding the external shocks to the industry of the terrorist attacks of 9/11/2001 [11], wars in Afghanistan and the Arabian Gulf and SARS. She emphasizes these negative factors have downward impacts on the demand for air travel. Matthiessen (2004) focuses on the internal and external accessibility of the Baltic Sea Area represented by air transport and discusses the challenges of hub and gateway development [12]. Sengupta et al. (2011) described development of a decision support system that uses real time track data to estimate statistical parameters describing the stochastic air traffic flow [13]. Onder and Hasgul (2009) used traditional time series analysis and Box Jenkins’ models and artificial neural network forecasting method to forecast international tourism arrivals to Turkey for 2008-2010 based on data period 1986-2007 [14]. They found that Winter’s seasonal exponential smoothing technique and artificial neural networks are two successful estimator methods for regarding monthly time series data. Carson et al. (2011) analyze whether it is better to forecast air travel demand using aggregate data at a national level, or to aggregate the forecasts derived for individual airports using airport-specific data [3]. 2. TRADITIONAL TECHNIQUES TIME SERIES In this study, two different traditional time series methods including decomposition methods and smoothing methods were applied to the macro economic data for forecasting. The methods and regarding formulas are shown in this section. The notation of Orhunbilge (1999) is used to explain the time series methods [15]. 2.1. Decomposition Methods Decomposition methods are using for determining secular trend, seasonal variation, conjuncture (cyclical variation) and random fluctuation (irregular variation) components in time series. It this study annual data was used. Therefore 3 important trend function including linear, quadratic and growth were mentioned in this part of this study. 2.1.1. Least Squares Method for Determining Trend Least square method is one of the popular method for determining trend. X is the time variable (year, month, etc.) in yt f ( x) function. If the the sum of the time series variable (X) is identified as zero the estimation values of model parameters can be shown ÖNDER, KUZU 66 Forecasting Air Traffic Volumes Using Smoothing Techniques (1) y na b x c x xy a x b x c x x y a x b x c x xy b x (2) 2.1.4. Growth Trend Function If the change of the y variable is nearly constant in time, growth trend function can be used for this kind of data. The growth trend function is shown below. as the following formulas. The trend of yt can be determined by least squares method. It is not easy to decide which function we should use as a trend. By trying several functions and finding minimum sum of squares of residuals, the suitable trend functions can be found. n n e y t t 1 t (11) 2 3 (12) t 2 2 3 4 t t yt min (13) (14) 2 2 2 2 t t 1 2.1.2. Linear Trend Function The linear trend function is shown as below: y a bx et When the least squares method is applied the linear trend function, the equations below are obtained. yt ab et x n (15) n e log y 2 n n e y t yt yt a bx 2 2 t 1 n t t 1 t 2 (3) t 1 t 1 t 2 log yt (16) t 1 n log yt log a x log b 0 2 (17) t 1 For determining the minimum of this function the first level derivatives should be done regarding to a and b parameters. y na b x xy a x b x (4) t 2 (5) t By solving these equations the parameters a and be can be found as follows: a b y t x (7) 2 2.1.3. Quadratic Trend Function If the observed data has a curved figure (in quadratic trend function the mean of the data is increasing first than start decreasing or reverse) than quadratic trend function can be used. y a bx cx et 2 n n e y 2 t t 1 t yt (8) 2 (9) t 1 n yt a bx cx 2 2 0 (10) t 1 First order derivatives of the equation according to a, b and c parameters should be solved for writing the quadratic trend function with using least squares method. The equations below are the normal equations. Three unknown can be found by solving these three equations. (18) t t t n x log yt log b x 2 log yt log a x log b (6) n xyt log y n log a log b x x log y log a x log b x log y log a 2 (19) (20) (21) (22) 2.2. Smoothing Methods Random or/and coincidental fluctuations in weekly, monthly, seasonal or annual time series data can be removed or softened by smoothing methods. Six smoothing methods including single moving averages, Brown’s simple exponential smoothing method, linear moving averages, Brown’s linear exponential smoothing methods with single parameter, Holt’s linear exponential smoothing with two parameters and Brown’s quadratic exponential smoothing methods are mentioned in this part of the study [5]. 2.2.1. Single Moving Averages Estimation can be done by using arithmetic mean of number of certain (k) prior period of data. Single moving average method gives the same importance level to the past data for estimating future values. yt1 yt1 yt1 ÖNDER, KUZU 67 ( yt yt 1 yt k 1 ) k 1 k yt k (23) t (24) yi i t k 1 yt k k yt (25) Forecasting Air Traffic Volumes Using Smoothing Techniques 2.2.2. Brown’s Simple Exponential Smoothing Method It is a suitable method for time series that y1 , y2 , , yn has no significant trend or seasonal fluctuations. yt is the estimation value for the time t. yt 1 is the observation data for the time t-1. is a smoothing constant. The constant has the value between 0 and 1. yt yt 1 (1 ) yt1 (26) yt yt 1 ( yt 1 yt1 ) (27) yt yt1 et (28) 2.2.3. Linear Moving Averages When moving averages method is applied the data which has a significant trend, estimations are always remains lower than actual values. To deal with this situation “Linear Moving Averages” method was developed. The main idea of this method is the calculation of second moving average. yt yt yt yt 1 yt 2 yt k 1 k yt yt1 yt 2 yt k 1 k at yt ( y yt ) 2 yt yt bt yˆ t m 2 ( yt yt) k 1 at bt m (29) (30) (31) (32) (33) The coefficient “m” is the forecast period to be estimated. 2.2.5. Holt’s Linear Exponential Smoothing Method with Two Parameter It seems similar to previous method (Brown’s Linear Exponential Smoothing Method with Single Parameter). But in Holt’s Linear Exponential Smoothing Method second smoothing is not used. Trend values are smoothed directly. This adds flexibility into the method. The parameters and have the values between 0 and 1. yt yt 1 yt1 bt 1 (39) bt yt yt1 1 bt 1 (40) yˆ t m yt bt m (41) The parameters and are the smoothing constants. These parameters should be optimized for minimizing the sum of error squares. 2.2.6. Brown’s Quadratic Exponential Smoothing Method When the time series are curved shape (quadratic, third order or more) Brown’s quadratic exponential smoothing technique is suitable for estimation. Third parameter is added to the model. The equations for quadratic exponential smoothing are below: yt yt 1 yt1 (42) yt yt 1 yt1 (43) yt yt 1 yt1 (44) at 3 yt 3 yt yt (45) bt 2 1 2 6 5 y 10 8 y 4 3 y t t t (46) 2.2.4. Brown’s Linear Exponential Smoothing Method with Single Parameter Brown’s Linear Exponential Smoothing Method with single parameter has some similarities with linear moving averages method. But the difference between first and second smoothing values is added into the first smoothing value. yt yt 1 yt1 (34) yt yt 1 yt1 (35) at yt yt yt 2 yt yt (36) bt yˆ t m yt yt 1 at bt m (37) (38) ct 2 1 2 y 2 y y t t (47) Estimation equation can be shown as below: yˆ t m at bt m 1 2 ct m 2 (48) The selection of α coefficient can be done as the selection in previous methods. 3. SEASONAL PARAMETERS VARIATIONS OF In this study Passenger/ Freight/ Flights statistical data in Turkey is extracted from the www.dhmi.gov.tr/ istatistik.aspx. Data are grouped by months and years in this web site. They are not categorized by airports. Therefore many Excel files were merged for obtaining airport based data. ÖNDER, KUZU 68 Forecasting Air Traffic Volumes Using Smoothing Techniques Table 1. Seasonal Indexes of Passenger/Freight/Total Aircraft/Commercial Aircraft Traffic in Turkey. Parameter Type Jan Feb Mar Apr May Jun Jul Domestic 90 88 91 96 104 110 120 117 106 100 90 88 Passenger International 50 48 64 79 117 137 163 166 143 117 65 53 Total 70 67 77 87 110 123 143 142 125 109 77 70 Domestic 85 83 84 89 100 113 129 129 112 101 89 86 International 61 61 77 85 112 123 142 144 129 114 79 73 Total 68 67 79 86 108 121 139 139 124 110 82 76 Domestic 87 82 94 96 108 111 119 115 104 102 93 89 Freight Total Aircraft Commercial Aircraft Aug Sep Oct Nov Dec International 63 59 73 86 114 128 145 146 129 115 76 67 Total 76 72 84 91 111 119 131 129 115 108 85 79 Domestic 92 86 94 97 104 108 116 113 104 102 93 92 International 63 58 72 85 115 129 146 147 130 114 75 67 Total 77 72 83 91 110 118 131 130 117 108 84 79 Seasonal variations are patterns of change in a time series within a period of time. These patterns tend to repeat themselves each period.The reason of these variations can be nature or human being. There are three important reasons for investigating seasonal variations. Short term variations can be explained, short term forecasting can be possible and seasonal effects can be distinguished from time series. Table 2. Seasonal Index of Domestic Passengers of Top 15 Airports in Turkey. ATATÜRK Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 89.0 87.1 91.1 96.5 103.0 108.6 120.2 116.7 108.3 103.1 88.6 87.7 SABIHA GÖKÇEN 93.4 89.5 89.3 95.1 105.4 111.8 121.4 112.3 104.7 96.6 90.3 90.2 ESENBOĞA 97.2 92.8 98.0 96.0 102.8 105.4 109.4 100.3 100.5 101.1 98.5 97.9 ADNAN MENDERES 94.7 93.4 94.8 98.7 105.4 105.4 112.7 108.4 101.0 97.8 94.1 93.7 ANTALYA 85.0 80.5 92.4 101.1 104.2 111.8 126.2 116.7 111.3 108.0 85.5 77.3 ADANA 103.0 97.9 96.9 98.0 101.8 101.6 105.7 101.8 97.8 98.2 97.6 99.9 TRABZON 95.9 91.6 91.2 91.2 98.8 106.6 121.6 113.3 104.5 95.2 94.9 95.3 DİYARBAKIR 102.0 97.6 99.5 95.4 101.6 99.0 109.7 98.4 100.8 95.6 101.7 98.7 MİLAS BODRUM 40.2 37.9 43.0 61.8 90.9 147.0 229.2 231.9 154.4 76.8 45.9 41.0 GAZİANTEP 98.0 94.1 96.9 98.5 104.9 102.0 106.1 102.7 103.4 101.3 97.5 94.7 SAMSUN ÇARŞAMBA 98.6 97.4 94.8 95.8 99.6 104.8 117.5 108.8 98.2 93.5 92.2 98.8 VAN F.MELEN 95.8 93.7 96.5 90.8 103.8 105.1 110.5 102.6 102.1 102.2 100.6 96.2 KAYSERİ 89.4 86.1 89.3 100.9 112.7 109.8 116.7 104.6 108.9 104.9 88.6 88.1 ERZURUM 103.5 96.6 96.2 92.3 99.5 106.3 114.0 101.9 97.0 99.0 98.6 95.0 DALAMAN 43.1 41.7 47.0 69.7 100.9 149.7 200.0 193.9 157.7 103.2 49.2 43.9 New and innovative projects and strategies should be organized to increase the capacity of airports including Atatürk, Sabiha Gokcen, Esenboga, Adnan Menderes and Antalya Airports for meeting estimated demand for the next 10 years due to Fig 1, Fig 2, Fig 3, Fig 4, Fig 5, Fig 6 and Fig 7. ÖNDER, KUZU 69 Forecasting Air Traffic Volumes Using Smoothing Techniques Figure 1. Total Domestic Passengers of Top 15 Airports in Turkey between Jan-2008 and June-2013. Table 3. Seasonal Index of International Passengers of Top 15 Airports in Turkey. Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec ATATÜRK 82.0 77.6 93.7 103.8 104.2 103.4 118.3 116.0 108.9 110.4 93.8 87.9 ANTALYA 15.4 20.3 36.5 61.5 134.7 170.4 197.0 204.4 173.3 130.7 39.4 16.5 SABIHA GÖKÇEN 75.3 72.6 82.8 96.8 99.7 104.6 135.5 131.7 116.4 112.2 89.1 83.2 .9 1.0 3.4 30.3 140.0 197.6 234.0 244.8 209.5 130.4 7.1 1.0 ADNAN MENDERES 40.3 42.5 57.6 78.4 111.4 136.0 180.1 185.0 151.9 114.9 55.7 46.5 MİLAS BODRUM 1.1 .6 1.8 36.1 133.0 195.7 241.2 254.3 210.1 119.2 5.2 1.8 ESENBOĞA 70.3 71.1 92.2 91.0 88.6 107.2 150.0 139.3 112.2 107.7 89.0 81.4 ADANA 78.7 84.9 98.3 98.0 91.5 104.4 135.0 135.7 108.1 96.1 86.3 83.1 KAYSERİ 46.8 46.8 71.0 81.1 79.6 113.8 210.0 203.4 123.2 103.0 58.7 62.5 GAZİANTEP 66.8 59.0 96.6 120.2 91.0 113.2 139.5 145.1 128.0 98.0 70.7 72.0 HATAY 122.2 94.6 92.1 80.6 92.7 66.0 78.7 89.5 94.4 118.5 137.4 133.1 SAMSUN ÇARŞAMBA 36.3 45.3 95.9 75.6 81.5 114.5 193.7 176.6 125.2 111.6 87.3 56.5 TRABZON 38.9 65.1 116.5 86.3 68.9 114.6 200.9 180.5 109.9 95.2 57.5 65.8 KONYA 21.2 34.1 156.6 114.7 41.6 117.1 244.4 205.3 89.7 62.9 47.7 64.5 NEVŞEHİR-KAPADOKYA 21.0 26.8 33.9 134.2 130.3 94.0 127.5 198.3 150.8 166.6 87.0 29.5 DALAMAN ÖNDER, KUZU 70 Forecasting Air Traffic Volumes Using Smoothing Techniques Figure 2. Total International Passengers of Top 15 Airports in Turkey between Jan-2008 and June-2013. Table 4. Seasonal Index of Domestic Cargo of Top 15 Airports in Turkey. Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec ATATÜRK 82.7 81.7 86.9 90.9 101.5 111.7 126.7 128.6 113.1 103.2 90.1 83.2 ANTALYA 82.1 76.4 89.6 94.9 101.6 116.9 134.5 121.3 110.6 110.8 82.9 78.5 A.MENDERES 91.9 87.2 88.3 94.6 100.6 104.6 120.6 118.8 108.9 99.1 93.3 92.0 SABIHA GÖKÇEN 88.8 87.0 74.8 84.2 93.2 113.0 137.7 132.2 114.5 95.3 93.8 85.5 ESENBOĞA 94.2 90.6 87.6 88.1 99.0 108.5 120.5 119.1 107.5 100.0 97.1 87.8 ADANA 100.0 94.1 91.4 93.2 95.8 101.2 113.2 115.3 102.7 99.0 99.1 95.0 TRABZON 89.0 89.1 80.9 80.1 87.4 106.2 137.1 130.4 114.1 94.0 96.4 95.3 DİYARBAKIR 96.9 95.4 90.3 92.0 94.5 98.9 119.0 108.9 106.9 94.0 108.1 95.3 MİLAS-BODRUM 32.9 30.3 32.1 50.1 85.4 151.9 250.8 255.3 166.7 74.3 39.1 31.2 GAZİANTEP 92.3 88.0 83.7 88.9 92.2 99.7 122.5 127.8 116.3 102.5 96.9 89.1 KAYSERİ 77.3 69.0 73.7 91.0 108.6 115.0 134.4 137.7 124.7 111.0 83.6 74.1 VAN F.MELEN 92.3 97.5 96.2 84.3 98.8 104.2 111.4 105.7 106.1 113.3 96.0 94.1 SAMSUN ÇARŞAMBA 96.5 94.4 81.4 83.3 88.7 104.7 137.4 127.3 109.6 89.4 95.4 91.8 DALAMAN 37.6 35.7 37.7 61.0 98.6 155.7 208.9 206.0 166.1 110.1 45.8 36.8 ERZURUM 105.6 107.6 91.0 81.7 93.3 108.6 120.2 108.4 99.8 94.2 97.9 91.9 ÖNDER, KUZU 71 Forecasting Air Traffic Volumes Using Smoothing Techniques Figure 3. Total Domestic Cargo of Top 15 Airports in Turkey between Jan-2008 and June-2013 (Unit: Ton). Table 5. Seasonal Index of International Cargo of Top 15 Airports in Turkey. Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec ATATÜRK 84.9 83.9 101.6 100.0 103.0 100.7 110.1 108.3 104.1 107.5 98.8 97.0 ANTALYA 16.0 20.5 37.9 62.7 134.5 169.5 195.8 198.8 173.4 132.7 40.3 17.7 SABIHA GÖKÇEN 71.0 73.1 81.5 87.4 96.0 97.0 120.7 124.2 120.3 124.9 111.7 92.2 .8 .9 3.1 27.6 142.4 198.2 229.3 240.1 215.5 134.4 6.7 1.2 ADNAN MENDERES 45.6 48.3 63.3 73.9 107.6 132.5 163.8 169.2 157.1 119.1 65.9 53.6 ESENBOĞA 68.2 70.2 92.1 85.1 86.5 107.6 145.3 137.5 115.0 107.2 92.5 92.7 DALAMAN MİLAS-BODRUM .3 .1 1.6 34.2 136.4 195.7 235.1 251.5 216.6 123.3 4.7 .5 TEKİRDAĞ/ ÇORLU 55.4 89.0 101.5 101.6 139.8 67.7 73.6 157.3 140.9 122.2 98.2 52.8 ADANA 71.6 86.5 104.2 90.0 84.6 101.6 137.6 146.6 108.6 94.7 95.1 78.8 KAYSERİ 46.4 43.6 70.9 79.5 80.3 114.6 200.8 206.6 129.8 104.2 58.0 65.2 GAZİANTEP 64.6 53.2 86.3 112.3 92.9 113.8 128.8 142.7 131.8 115.2 78.0 80.4 TRABZON 37.3 58.1 125.0 88.3 70.6 105.1 195.9 171.7 108.3 97.5 63.5 78.7 SAMSUN ÇARŞAMBA 34.2 34.6 83.2 99.2 81.7 109.9 189.7 176.6 107.3 101.1 118.3 64.1 KONYA 16.3 14.5 153.0 118.0 45.7 97.9 244.0 207.0 111.2 63.4 59.7 69.4 BURSA-YENİŞEHIR 71.0 68.9 246.9 158.5 71.3 66.3 90.0 111.6 70.5 86.3 133.4 25.3 ÖNDER, KUZU 72 Forecasting Air Traffic Volumes Using Smoothing Techniques Figure 4. Total International Cargo of Top 15 Airports in Turkey between Jan-2008 and June-2013 (Unit: Ton). 4. FORECASTING Smoothing methods have good short-term accuracy. Also their simplicity is one of the other advantages. Large amount of historical data are not required. However in smoothing methods choosing smoothing coefficient (α and/or γ) properly is very important. It affects the quality of forecasting. For determining these coefficients Excel Solver tool is used. The data in this study is more convenient to curve estimation tool of SPSS 13 package program. For method selection process average squares of residuals are used. Methods with minimum average squares of residuals are selected for both curve estimation and smoothing. In curve estimation, for all three variables (Passenger Traffic, Flight Traffic, Freight Traffic) cubic curve estimation methods are selected for forecasting. In Appendix 1, details of method selection process can be seen for all variables. For instance, in this table (Appendix 1A) minimum error square of passenger traffic variable is 4,905,512,522,046 (cubic curve estimation’s average squares of residuals). Cubic curve estimation method also was selected for “Flight Traffic” and “Freight Traffic” variables. In smoothing methods, Holt’s Linear Exponential Smoothing Method with Two Parameter method is selected for Passenger Traffic variable, Brown’s Linear Exponential Smoothing Method with Single Parameter method is selected for Flight Traffic and Linear Moving Averages method is selected for Freight Traffic. Air transport is the most important medium for long distance transport of passengers and freights and has strategic significance for global accessibility [6]. The statistics already presented show that the last 10 years (2002-2012) has seen significant development occur in the airline industry. This increase in domestic and international traffic may be due to either falling prices in all product classes or increase number of airports/ airplane firms etc. Aviation sector in Turkey has shown a tremendous growth in air travel demand and in the number of flights in last decade that can be seen in Table 6, Table 8 and Table 10. ÖNDER, KUZU 73 Forecasting Air Traffic Volumes Using Smoothing Techniques Passenger Traffic Statistics in All Airports of Turkey during 20022012 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 33,783,892 34,443,655 45,057,371 55,572,426 61,655,659 70,296,532 79,438,289 85,508,508 102,800,392 117,620,469 130,351,620 8,729,279 9,147,439 14,460,864 20,529,469 28,774,857 31,949,341 35,832,776 41,226,959 50,575,426 58,258,324 64,721,316 25,054,613 25,296,216 30,596,507 35,042,957 32,880,802 38,347,191 43,605,513 44,281,549 52,224,966 59,362,145 65,630,304 Passenger Traffic Estimations in All Airports of Turkey for 2013-2023 Table 6. Domestic and International Passenger Traffic Estimation in Turkey (Curve Estimation: Cubic). Passenger Passenger Passenger Year Traffic Traffic Traffic (Domestic) (International) 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 148,773,323 168,672,019 191,071,288 216,192,734 244,257,965 275,488,585 310,106,200 348,332,416 390,388,840 436,497,077 486,878,732 73,122,450 81,782,874 90,967,037 100,693,266 110,979,883 121,845,214 133,307,582 145,385,313 158,096,730 171,460,158 185,493,921 75,650,873 86,889,146 100,104,250 115,499,469 133,278,082 153,643,371 176,798,618 202,947,104 232,292,110 265,036,919 301,384,811 Figure 5. Domestic and International Passenger Traffic Estimation in Turkey (Curve Estimation: Cubic). ÖNDER, KUZU 74 Forecasting Air Traffic Volumes Using Smoothing Techniques Table 7. Domestic and International Passenger Traffic Estimation in Turkey (Holt’s Linear Exponential Smoothing Method with Two Parameter). Passenger Traffic Statistics in All Airports of Turkey during 20022012 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Passenger Traffic Estimations in All Airports of Turkey for 2013-2023 Year 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 Passenger Traffic 33,783,892 34,443,655 45,057,371 55,572,426 61,655,659 70,296,532 79,438,289 85,508,508 102,800,392 117,620,469 130,351,620 143,708,121 157,043,732 170,379,344 183,714,956 197,050,567 210,386,179 223,721,790 237,057,402 250,393,014 263,728,625 277,064,237 Passenger Traffic (Domestic) 8,729,279 9,147,439 14,460,864 20,529,469 28,774,857 31,949,341 35,832,776 41,226,959 50,575,426 58,258,324 64,721,316 71,671,252 78,608,988 85,546,725 92,484,462 99,422,198 106,359,935 113,297,672 120,235,408 127,173,145 134,110,882 141,048,618 Passenger Traffic (International) 25,054,613 25,296,216 30,596,507 35,042,957 32,880,802 38,347,191 43,605,513 44,281,549 52,224,966 59,362,145 65,630,304 72,036,869 78,434,744 84,832,619 91,230,494 97,628,369 104,026,244 110,424,118 116,821,994 123,219,869 129,617,743 136,015,619 Figure 6. Domestic and International Passenger Traffic Estimation in Turkey (Holt’s Linear Exponential Smoothing Method with Two Parameter). ÖNDER, KUZU 75 Forecasting Air Traffic Volumes Using Smoothing Techniques Table 8. Domestic and International Flight Traffic Estimation in Turkey (Curve Estimation: Cubic). Flight Traffic Flight Traffic Statistics in All Airports of Turkey during 20022012 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 376,579 374,987 449,493 551,980 627,401 688,468 741,765 788,469 919,411 1,042,369 1,093,047 157,953 156,582 196,207 265,113 341,262 365,177 385,764 419,422 497,862 579,488 600,818 218,626 218,405 253,286 286,867 286,139 323,291 356,001 369,047 421,549 462,881 492,229 Flight Traffic Estimations in All Airports of Turkey for 2013-2023 Flight Traffic (Domestic) Year Flight Traffic (International) 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 1,206,595 1,313,183 1,425,177 1,542,706 1,665,900 1,794,888 1,929,800 2,070,766 2,217,915 2,371,377 2,531,282 665,209 723,028 782,226 842,734 904,480 967,396 1,031,411 1,096,455 1,162,458 1,229,350 1,297,062 541,387 590,155 642,951 699,972 761,420 827,492 898,390 974,312 1,055,458 1,142,027 1,234,220 Figure 7. Domestic and International Flight Traffic Estimation in Turkey (Curve Estimation: Cubic). ÖNDER, KUZU 76 Forecasting Air Traffic Volumes Using Smoothing Techniques Table 9. Domestic and International Flight Traffic Estimation in Turkey (Brown’s Linear Exponential Smoothing Method with Single Parameter). Flight Traffic Flight Traffic Statistics in All Airports of Turkey during 20022012 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 376,579 374,987 449,493 551,980 627,401 688,468 741,765 788,469 919,411 1,042,369 1,093,047 157,953 156,582 196,207 265,113 341,262 365,177 385,764 419,422 497,862 579,488 600,818 Flight Traffic Estimations in All Airports of Turkey for 2013-2023 Flight Traffic (Domestic) Year 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 1,145,173 1,197,291 1,249,409 1,301,528 1,353,646 1,405,765 1,457,883 1,510,002 1,562,120 1,614,238 1,666,357 623,353 645,882 668,410 690,939 713,468 735,997 758,525 781,054 803,583 826,112 848,640 Flight Traffic (International) 218,626 218,405 253,286 286,867 286,139 323,291 356,001 369,047 421,549 462,881 492,229 521,820 551,409 580,999 610,589 640,178 669,768 699,358 728,948 758,537 788,126 817,717 Figure 8. Domestic and International Flight Traffic Estimation in Turkey (Brown’s Linear Exponential Smoothing Method with Single Parameter). ÖNDER, KUZU 77 Forecasting Air Traffic Volumes Using Smoothing Techniques Table 10. Domestic and International Freight Traffic Estimation in Turkey (Curve Estimation: Cubic). Freight Traffic Freight Traffic Statistics in All Airports of Turkey during 2002-2012 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 896,865 964,080 1,164,349 1,304,241 1,360,550 1,546,184 1,644,014 1,726,345 2,021,076 2,249,473 2,249,133 181,262 188,979 262,790 324,597 389,206 414,294 424,555 484,833 554,710 617,834 633,076 715,603 775,101 901,559 979,644 971,344 1,131,890 1,219,459 1,241,512 1,466,366 1,631,639 1,616,057 Freight Traffic Estimations in All Airports of Turkey for 2013-2023 Freight Traffic (Domestic) Year Freight Traffic (International) 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2,493,676 2,681,903 2,878,889 3,085,018 3,300,676 3,526,249 3,762,123 4,008,682 4,266,313 4,535,401 4,816,331 696,349 750,424 807,391 867,692 931,767 1,000,058 1,073,007 1,151,056 1,234,644 1,324,215 1,420,208 1,797,326 1,931,479 2,071,497 2,217,326 2,368,909 2,526,191 2,689,115 2,857,627 3,031,669 3,211,186 3,396,122 Figure 9. Domestic and International Freight Traffic Estimation in Turkey (Curve Estimation: Cubic). ÖNDER, KUZU 78 Forecasting Air Traffic Volumes Using Smoothing Techniques Table 11. Domestic and International Freight Traffic Estimation in Turkey (Linear Moving Averages). Freight Traffic Freight Traffic Statistics in All Airports of Turkey during 2002-2012 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 896,865 964,080 1,164,349 1,304,241 1,360,550 1,546,184 1,644,014 1,726,345 2,021,076 2,249,473 2,249,133 181,262 188,979 262,790 324,597 389,206 414,294 424,555 484,833 554,710 617,834 633,076 Freight Traffic Estimations in All Airports of Turkey for 2013-2023 Freight Traffic (Domestic) Year 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2,540,124 2,723,572 2,907,021 3,090,469 3,273,918 3,457,366 3,640,814 3,824,263 4,007,711 4,191,159 4,374,608 710,710 765,128 819,547 873,965 928,383 982,802 1,037,220 1,091,638 1,146,057 1,200,475 1,254,893 Freight Traffic (International) 715,603 775,101 901,559 979,644 971,344 1,131,890 1,219,459 1,241,512 1,466,366 1,631,639 1,616,057 1,829,414 1,958,444 2,087,474 2,216,504 2,345,535 2,474,564 2,603,594 2,732,625 2,861,654 2,990,684 3,119,715 Figure 10. Domestic and International Freight Traffic Estimation in Turkey (Linear Moving Averages). ÖNDER, KUZU 79 Forecasting Air Traffic Volumes Using Smoothing Techniques critique of the aerotropolis model, Futures 39, 1009 – 1028 5. CONCLUSION AND SUGGESTIONS Forecasting techniques are important tools in operational management for creating realistic expectations. In literature many different techniques in the area of statistics and artificial intelligence were proposed for achieving close estimations. In this study, cubic curve estimation method is selected for forecasting “Passenger Traffic”, “Flight Traffic” and “Freight Traffic” variables. The reason of this is cubic curve estimation method has higher order polynomial function than other curve fitting methods. Therefore it has more coefficients and this decreases the average squares of residuals. Also in smoothing methods, Holt’s Linear Exponential Smoothing Method with Two Parameter is selected for Passenger Traffic variable, Brown’s Linear Exponential Smoothing Method with Single Parameter is selected for Flight Traffic variable and Linear Moving Averages method is selected for Freight Traffic variable. Aviation sector in Turkey has shown a tremendous growth in air travel demand and in the number of flights in last decade. Airport planning includes capacity, local and global planning, aviation traffic forecasting, and airspace planning. One of the important statistical tools of capacity planning is obtaining seasonal indexes of all airports. For instance Milas Bodrum Airport has international passenger seasonal indexes of 1.8 for March and 254.3 for August. These seasonal airports can be effective when they maximize their productivity with accurate capacity planning using quantitative techniques. The seasonal index can also be used to derive an improved, seasonally adjusted forecast for logistic demands. With Ataturk Airport and Sabiha Gokcen Airport Istanbul is one of the most important air hub cities in the world. Also third airport of Istanbul will be constructed including six runways, 16 taxiways, 88 passenger bridges, 165 aircraft passenger bridges at all terminals and a 6.5 million-square-meter apron with capacity for 500 aircraft.. Once all six of the planned runways are complete, the capacity is expected to increase to 150 million passengers, one of the world’s largest in terms of the passenger capacity at full capacity. When we check the forecasting numbers the third airport is necessary for Istanbul. 6. REFERENCES [1] Gracht, H.A. and Darkow, I.L., (2010). Scenarios for the logistics services industry: A Delphibased analysis for 2025, Int. J. Production Economics 127, 46–59 [2] Charles, M.B., Barnes, P., Ryanb, N. and Clayton, J., (2007). Airport futures: Towards a [3] Carson, R.T., Cenesizoglu, T. and Parker, R., (2011).Forecasting (aggregate) demand for US commercial air travel, International Journal of Forecasting 27, 923–941 [4] China,A.T.H., Tay, J.H., (2001). Developments in air transport: implications on investment decisions, profitability and survival of Asian airlines, Journal of Air Transport Management 7, 319–330 [5] Adrangi, B., Chatrath, A. and Raffiee, K., (2001). The demand of US air transport service: a chaos and nonlinearity investigation, Transportation Research, Part E, 37, 337-353 [6] Jonga, G., Gunnc, H. and Akiva, M.B., (2004). A meta-model for passenger and freight transport in Europe Transport Policy 11, 329–344 [7] Matsumoto, H., (2004). International urban systems and air passenger and cargo flows: some calculations, Journal of Air Transport Management 10, 241–249 [8] Lee, H. S., (2009). The networkability of cities in the international air passenger flows 1992–2004. Journal of Transport Geography 17, 166–175 [9] Hui, G W. L., Hui, Y. V. and Zhang, A., (2004). Analyzing China’s air cargo flows and data. Journal of Air Transport Management 10, 125–135 [10] Hwang, C. C., Shiao, G. C., (2011). Analyzing air cargo flows of international routes: an empirical study of Taiwan Taoyuan International Airport. Journal of Transport Geography 19, 738–744 [11] Mason, K.J., (2005). Observations of fundamental changes in the demand for aviation services. Journal of Air Transport Management 1, 19– 25 [12] Matthiessen, C.W., (2004). International air traffic in the Baltic Sea Area: Hub-gateway status and prospects. Copenhagen in focus. Journal of Transport Geography 12, 197–206 [13] Sengupta, P., Tandale, M., Cheng, V., Menon, P., (2011) .Air Traffic Estimation and Decision Support for Stochastic Flow Management, American Institute of Aeronautics and Astronautics Guidance, Navigation, and Control Conference, 8-11 August 2011, Portland, Oregon [14] Önder, E., Hasgül, O., 2009. Time Series Analysis with Using Box Jenkins Models and Artificial Neural Network for Forecasting Number of Foreign Visitors. Journal of Institute of Business Administration - Yönetim (20), 62, 62-83 [15] Orhunbilge, N., 1999, Time Series Analysis, Forecasting and Price Index. Istanbul University, School of Business Press, Publication No: 277, 11– 130. (In Turkish) ÖNDER, KUZU 80 Forecasting Air Traffic Volumes Using Smoothing Techniques [16] www.dhmi.gov.tr/istatistik.aspx (17.09.2013) VITAE Emrah ÖNDER He graduated as an electronic engineer from I.U. Electronic Engineering Department, and received a MSc and PhD degree from the I.U. School of Business, Department of Quantitative Methods. He also received MBA diploma from Ball State University, Indiana/USA. He is currently a research and teaching assistant of I.U. School of Business. His dominant scientific interest focuses on: quantitative methods. Sultan KUZU She graduated from Anadolu University, Business Faculty and received a BSc and MSc in Mathematics Teacher Education in Marmara University, Ataturk Education Faculty. She is currently a research and teaching assistant and PhD student of I.U. School of Business. Her dominant scientific interest focuses on: statistics. ÖNDER, KUZU 81 2. Smoothing 1. Curve Estimation Holt’s Linear Exponential Smoothing Method with Two Parameter Brown’s Quadratic Exponential Smoothing Method Brown’s Linear Exponential Smoothing Method with Single Parameter Linear Moving Averages 0.440 0.990 0.820 0.010 29,427,216.370 0.609 0.139 0.139 82 ÖNDER, KUZU β1 β1 -1.391 β2 β2 β2 β2 β2 -190,151.700 474,665.740 β3 β3 β3 β3 β3 β3 β3 β3 β3 36934.302 8,583,577,323,259 8,583,577,323,259 384,538,387,801,016 84,896,370,558,236 8,583,577,323,259 4,905,512,522,046 5,671,615,054,744 466,148,283,099,064 184,449,052,023,090 28,610,613,734,751 26,844,822,909,517 27,574,775,683,477 27,637,885,504,028 2,695,382,614,092,580 Constant Exponential 17.197 β1 0.595 β2 β2 β2 β2 β3 Brown’s Simple Exponential Smoothing Method Constant Growth 18.411 β1 1.149 7,330,301.118 β1 β1 3,998,827.055 -86,599,520.400 β1 β1 39,278,818.418 β2 Average (e2 ) 23,245,605,105,802 446,755,763,202,740 Constant S 26,225,404.830 29,427,216.370 98,004,431.158 β1 β1 Parameters 9,694,815.936 Single Moving Averages Constant Constant Constant Cubic Power 24,369,079.909 Constant Quadratic Compound 28,402,305.715 Constant Inverse 11,732,621.930 Constant Logarithmic 16,060,996.473 Constant Linear Method APPENDIX 1 A. Model selection using average squares of residuals (Passenger Traffic) Forecasting Air Traffic Volumes Using Smoothing Techniques Selected Selected Selection 2. Smoothing 1. Curve Estimation Holt’s Linear Exponential Smoothing Method with Two Parameter Brown’s Quadratic Exponential Smoothing Method Brown’s Linear Exponential Smoothing Method with Single Parameter Linear Moving Averages 0.422 0.990 0.990 0.050 331,431.060 0.990 0.113 0.113 83 ÖNDER, KUZU β1 β1 -1.128 β2 β2 β2 β2 β2 1,860.288 2,249.131 β3 β3 β3 β3 β3 β3 β3 β3 β3 21.602 964,827,282 964,827,282 21,645,856,879 4,587,184,376 964,827,282 598,748,263 599,010,342 26,193,439,739 9,450,003,643 2,908,780,832 2,251,419,185 2,227,454,502 2,531,252,630 130,461,326,204 Constant Exponential 12.711 β1 0.485 β2 β2 β2 β2 β3 Brown’s Simple Exponential Smoothing Method Constant Growth 13.700 β1 1.120 49,949.549 β1 β1 48,001.015 -684,342.968 β1 β1 307,677.954 β2 Average (e2 ) 993,580,220 26,465,530,814 Constant S 301,818.123 331,431.060 883,690.984 β1 β1 Parameters 74,990.582 Single Moving Averages Constant Constant Constant Cubic Power 301,990.288 Constant Quadratic Compound 304,349.267 Constant Inverse 206,263.157 Constant Logarithmic 245,871.873 Constant Linear Method APPENDIX 1 B. Model selection using average squares of residuals (Flight Traffic) Forecasting Air Traffic Volumes Using Smoothing Techniques Selected Selected Selection 2. Smoothing 1. Curve Estimation Holt’s Linear Exponential Smoothing Method with Two Parameter Brown’s Quadratic Exponential Smoothing Method Brown’s Linear Exponential Smoothing Method with Single Parameter Linear Moving Averages (k=3) 0.334 0.990 0.594 0.990 845,180.560 0.165 0.094 0.094 84 ÖNDER, KUZU β1 β1 -0.970 β2 β2 β2 β2 β2 1,872.997 3,029.640 β3 β3 β3 β3 β3 β3 β3 β3 β3 64.258 4,261,826,952 4,261,826,952 71,889,235,380 15,961,066,122 4,261,826,952 3,073,180,263 3,075,499,156 86,568,675,890 30,050,753,944 14,468,529,780 11,228,609,810 14,176,570,816 10,478,903,214 26,080,672,793 Constant Exponential 13.647 β1 0.409 β2 β2 β2 β2 β3 Brown’s Simple Exponential Smoothing Method Constant Growth 14.480 β1 1.099 111,265.526 β1 β1 105,469.458 -1,336,457.528 β1 β1 588,642.092 β2 Average (e2 ) 3,791,439,126 90,251,202,919 Constant S 777,244.320 845,180.560 1,923,840.710 β1 β1 Parameters 141,825.136 Single Moving Averages Constant Constant Constant Cubic Power 777,740.121 Constant Quadratic Compound 784,757.091 Constant Inverse 620,337.717 Constant Logarithmic 705,986.455 Constant Linear Method APPENDIX 1 C. Model selection using average squares of residuals (Freight Traffic) Forecasting Air Traffic Volumes Using Smoothing Techniques Selected Selected Selection Forecasting Air Traffic Volumes Using Smoothing Techniques APPENDIX 2: Curve estimation algorithms (SPSS 13.0 for Windows) ÖNDER, KUZU 85

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