FORECASTING AIR TRAFFIC VOLUMES USING SMOOTHING TECHNIQUES

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1 JOURNAL OF AERONAUTICS AND SPACE TECHNOLOGIES JANUARY 014 VOLUME 7 NUMBER 1 (65-85) FORECASTING AIR TRAFFIC VOLUMES USING SMOOTHING TECHNIQUES Emrah ÖNDER * Isanbul Universiy, School of Business, Quaniaive Techniques Deparmen, Isanbul, Turkey Sulan KUZU Isanbul Universiy, School of Business, Quaniaive Techniques Deparmen, Isanbul, Turkey Received:, nd Ocober 013 Acceped: 16 h January 014 ABSTRACT For many years, researchers have been using saisical ools o esimae parameers of macroeconomic models. Forecasing plays a major role in logisic planning and i is an essenial analyical ool in counries air raffic sraegies. In recen years, researchers are developing new echniques for esimaion. In paricular, his research focuses on he applicaion of smoohing echniques and esimaion of air raffic volume. In his sudy four air raffic indicaors including oal passenger raffic, oal cargo raffic, oal fligh raffic and commercial fligh raffic were used for forecasing. Also seasonal effecs of hese parameers were invesigaed. As analysis ools, classical ime series forecasing mehods such as moving averages, exponenial smoohing, Brown's single parameer linear exponenial smoohing, Brown s second-order exponenial smoohing, Hol's wo parameer linear exponenial smoohing and decomposiion mehods applied o air raffic volume daa beween January 007 and May 013. The sudy focuses mainly on he applicabiliy of Tradiional Time Series Analysis (Smoohing & Decomposiion Techniques). To faciliae he presenaion, an empirical example is developed o forecas Turkey s four imporan air raffic parameers. Time Series saisical heory and mehods are used o selec an adequae echnique, based on residual analysis. Keywords: Air Volume, Forecasing, Smoohing, Decomposiion, Time Series, Turkey. HAVA TRAFİK YOĞUNLUĞUNUN DÜZGÜNLEŞTİRME YÖNTEMLERİ İLE TAHMİNİ ÖZET Uzun yıllardır araşırmacılar makroekonomik modellere ai paramerelerin ahmininde isaisik araçlar kullanırlar. Tahminleme lojisik planlamada önemli bir yere sahipir ve ülkelerin hava rafik sraejilerinin belirlenmesinde kullanılan bir sayısal yönemdir. Bu araşırmada özellikle düzgünleşirme ekniklerinin uygulanabilirliği ve hava rafik yoğunluğunun ahminlenmesine odaklanılmışır. Çalışma kapsamında oplam yolcu rafiği, oplam kargo rafiği, oplam uçak rafiği ve oplam icari uçak rafiği olmak üzere dör hava rafik yoğunluğu parameresi incelenmişir. Bunun yanı sıra bu paramerelere ai mevsimsel ekiler espi edilmişir. İsaisik analiz araçları olarak harekeli oralamalar, üsel düzgünleşirme, Brown ın ek paramereli doğrusal üsel düzgünleşirme yönemi, Brown ın ikinci derece üsel düzgünleşirme yönemi, Hol un iki paramereli doğrusal üsel düzgünleşirme yönemi ve zaman serilerinin bileşenlere ayırma yönemleri gibi klasik zaman serisi yönemleri Ocak 007-Mayıs 013 döneminde gerçeklesen hava rafik yoğunluğu üzerinde uygulanmışır. Araşırmada klasik zaman serisi yönemlerinin (Düzgünleşirme ve Ayrışırma) uygulanabilirliği üzerinde durulmuşur. Uygulamada Türkiye hava rafik yoğunluğuna ai dör paramere kullanılmışır. Zaman serisi isaisiki alyapısı, meoları ve haa oralamasından yararlanılarak uygun ekniğin seçimini sağlamışır. Anahar Kelimeler: Hava Trafik Yoğunluğu, Tahminleme, Düzgünleşirme, Zaman Serileri, Türkiye. * Corresponding Auhor 65

2 1. INTRODUCTION Forecasing is he cener ool of he planning and conrol processes. The objecive of forecasing is o provide informaion ha can be used o evaluae and clarify he effecs of uncerainy abou he fuure. Thus, financial planning and resource allocaion can be done successfully. The logisics services indusry will be significanly affeced by fuure developmens hroughou he world [1]. I is esimaed ha his cenury will be dominaed by air ranspor, boh for domesic and inernaional carriage of passengers and freigh []. Air ranspor is an imporan par of logisic secor. Therefore, developing saisical analysis and forecasing ools are key elemens for long-erm sraegy developmen and decision suppor sysems for logisic decision makers. Bu here are no sufficien logisics researches abou air raffic forecasing. In his paper, we apply forecasing echniques o he air raffic daa for he fuure of he air logisics services indusry ill he year 03. The sraegic decisions of airlines involve analysis such as air raffic forecasing, he cycles of orders and deliveries, airline design [3], producion planning, research and developmen, profi cycles, airline growh and survivabiliy [4]. Alhough here are no many air raffic forecasing researches in lieraure, some of he sudies are shown below. Adrangi, e al. (001) examines he behavior of he US airline indusry s service demand using GARCH models [5]. Jonga e al. (004) develop mea-model includes forecasing and simulaion for passenger and freigh ranspor in Europe [6]. Masumoo s research (004) examines inernaional urban sysems from he sandpoin of inernaional air raffic flows and analyzes he paerns of inernaional air passenger and cargo flows wihin and among he Asian, European and American regions from 198 o 1998 [7]. This paper s resuls reveal ha Tokyo, Hong Kong and Singapore in Asia, London, Paris, Frankfur and Amserdam in Europe and New York and Miami in he US are srenghening heir posiions as inernaional hubs. Lee (009) proposed a modified social nework analysis model for use in he examinaion of he inernaional air nework by esimaing conneciviy of he air roues, using he air raffic and he number of air roues [8]. Wih analyzing daa, i was observed ha London, Paris, Frankfur, Amserdam, and New York were firs class ciies ha were a he op in boh years. Hui e al. (004) provides an analysis of China s air cargo flows idenifies major air ranspor hubs in China and examines cargo movemens beween hem [9]. Their paper shows overall saisics on China s aviaion and describes air cargo rends in China. Hwang and Shiao (011) develop a graviy model of air cargo flows based on he panel daa of air cargo services on scheduled roues a Taiwan Taoyuan Inernaional Airpor during he years [10]. Their resuls indicae ha populaion, air freigh rae and hree dummy variables, including he regional economic bloc of he Chinese Circle (an informal parnership beween Hong Kong, Macao, Taiwan and mainland China), he Open Sky Agreemens and long esablished colonial links, are key deerminans of inernaional air cargo flows from/o Taiwan. Mason (005) addresses he inexorable decline in yield in he airline indusry regarding he exernal shocks o he indusry of he erroris aacks of 9/11/001 [11], wars in Afghanisan and he Arabian Gulf and SARS. She emphasizes hese negaive facors have downward impacs on he demand for air ravel. Mahiessen (004) focuses on he inernal and exernal accessibiliy of he Balic Sea Area represened by air ranspor and discusses he challenges of hub and gaeway developmen [1]. Sengupa e al. (011) described developmen of a decision suppor sysem ha uses real ime rack daa o esimae saisical parameers describing he sochasic air raffic flow [13]. Onder and Hasgul (009) used radiional ime series analysis and Box Jenkins models and arificial neural nework forecasing mehod o forecas inernaional ourism arrivals o Turkey for based on daa period [14]. They found ha Winer s seasonal exponenial smoohing echnique and arificial neural neworks are wo successful esimaor mehods for regarding monhly ime series daa. Carson e al. (011) analyze wheher i is beer o forecas air ravel demand using aggregae daa a a naional level, or o aggregae he forecass derived for individual airpors using airpor-specific daa [3].. TRADITIONAL TIME SERIES TECHNIQUES In his sudy, wo differen radiional ime series mehods including decomposiion mehods and smoohing mehods were applied o he macro economic daa for forecasing. The mehods and regarding formulas are shown in his secion. The noaion of Orhunbilge (1999) is used o explain he ime series mehods [15]..1. Decomposiion Mehods Decomposiion mehods are using for deermining secular rend, seasonal variaion, conjuncure (cyclical variaion) and random flucuaion (irregular variaion) componens in ime series. I his sudy annual daa was used. Therefore 3 imporan rend funcion including linear, quadraic and growh were menioned in his par of his sudy Leas Squares Mehod for Deermining Trend Leas square mehod is one of he popular mehod for deermining rend. X is he ime variable (year, monh, ec.) in y f( x) funcion. If he he sum of he ime series variable (X) is idenified as zero he esimaion values of model parameers can be shown 66

3 as he following formulas. The rend of y can be deermined by leas squares mehod. I is no easy o decide which funcion we should use as a rend. By rying several funcions and finding minimum sum of squares of residuals, he suiable rend funcions can be found. n n e y y min (1) Linear Trend Funcion The linear rend funcion is shown as below: y abx e () When he leas squares mehod is applied he linear rend funcion, he equaions below are obained. n n n e y y y abx (3) For deermining he minimum of his funcion he firs level derivaives should be done regarding o a and b parameers. y nab x (4) xy a xb x (5) By solving hese equaions he parameers a and be can be found as follows: y na b x c x (11) 3 xy a x b x c x (1) 3 4 x y a x b x c x (13) b xy x (14).1.4. Growh Trend Funcion If he change of he y variable is nearly consan in ime, growh rend funcion can be used for his kind of daa. The growh rend funcion is shown below. x y ab e n (15) n e log y log y (16) 1 1 n log y log a xlog b 0 (17) 1 log y nlog alog b x (18) x log y log a xlog b x (19) log y log a (0) n log b x log y x (1) log y log a xlog b () y a (6) n b xy x (7).1.3. Quadraic Trend Funcion If he observed daa has a curved figure (in quadraic rend funcion he mean of he daa is increasing firs han sar decreasing or reverse) han quadraic rend funcion can be used. y abxcx e (8) n n e y y (9) 1 1 n 1 y a bx cx 0 (10) Firs order derivaives of he equaion according o a, b and c parameers should be solved for wriing he quadraic rend funcion wih using leas squares mehod. The equaions below are he normal equaions. Three unknown can be found by solving hese hree equaions... Smoohing Mehods Random or/and coincidenal flucuaions in weekly, monhly, seasonal or annual ime series daa can be removed or sofened by smoohing mehods. Six smoohing mehods including single moving averages, Brown s simple exponenial smoohing mehod, linear moving averages, Brown s linear exponenial smoohing mehods wih single parameer, Hol s linear exponenial smoohing wih wo parameers and Brown s quadraic exponenial smoohing mehods are menioned in his par of he sudy [5]...1. Single Moving Averages Esimaion can be done by using arihmeic mean of number of cerain (k) prior period of daa. Single moving average mehod gives he same imporance level o he pas daa for esimaing fuure values. y 1 ( y y y ) 1 k1 k 1 (3) y y 1 i k i k1 (4) y y k y y 1 k k (5) 67

4 ... Brown s Simple Exponenial Smoohing Mehod I is a suiable mehod for ime series ha y1, y,, yn has no significan rend or seasonal flucuaions. y is he esimaion value for he ime. y 1is he observaion daa for he ime -1. is a smoohing consan. The consan has he value beween 0 and 1. y y (1 ) y (6) 1 1 y y ( y y ) (7) y y e (8) Linear Moving Averages When moving averages mehod is applied he daa which has a significan rend, esimaions are always remains lower han acual values. To deal wih his siuaion Linear Moving Averages mehod was developed. The main idea of his mehod is he calculaion of second moving average. y y y y y 1 k1 k (9) y y y y 1 k1 y (30) k a y( y y) y y (31) b ( y y ) k 1 (3) yˆ m a bm (33) The coefficien m is he forecas period o be esimaed...4. Brown s Linear Exponenial Smoohing Mehod wih Single Parameer Brown s Linear Exponenial Smoohing Mehod wih single parameer has some similariies wih linear moving averages mehod. Bu he difference beween firs and second smoohing values is added ino he firs smoohing value y y y (34) y y y (35) a y y y y y (36) b y y 1 (37) yˆ m a bm (38)..5. Hol s Linear Exponenial Smoohing Mehod wih Two Parameer I seems similar o previous mehod (Brown s Linear Exponenial Smoohing Mehod wih Single Parameer). Bu in Hol s Linear Exponenial Smoohing Mehod second smoohing is no used. Trend values are smoohed direcly. This adds flexibiliy ino he mehod. The parameers and have he values beween 0 and y y y b (39) b y y b (40) 1 1 y y bm (41) ˆ m The parameers and are he smoohing consans. These parameers should be opimized for minimizing he sum of error squares...6. Brown s Quadraic Exponenial Smoohing Mehod When he ime series are curved shape (quadraic, hird order or more) Brown s quadraic exponenial smoohing echnique is suiable for esimaion. Third parameer is added o he model. The equaions for quadraic exponenial smoohing are below: y y y (4) yy y (43) yy y (44) a 3y 3y y (45) b 65 y 108 y 43 y 1 (46) c y y y 1 Esimaion equaion can be shown as below: 1 yˆ a bm cm (47) (48) m The selecion of α coefficien can be done as he selecion in previous mehods. 3. SEASONAL VARIATIONS OF PARAMETERS In his sudy Passenger/ Freigh/ Flighs saisical daa in Turkey is exraced from he isaisik.aspx. Daa are grouped by monhs and years in his web sie. They are no caegorized by airpors. Therefore many Excel files were merged for obaining airpor based daa. 68

5 Table 1. Seasonal Indexes of Passenger/Freigh/Toal Aircraf/Commercial Aircraf in Turkey. Parameer Type Jan Feb Mar Apr May Jun Jul Aug Sep Oc Nov Dec Passenger Freigh Toal Aircraf Commercial Aircraf Domesic Inernaional Toal Domesic Inernaional Toal Domesic Inernaional Toal Domesic Inernaional Toal Seasonal variaions are paerns of change in a ime series wihin a period of ime. These paerns end o repea hemselves each period.the reason of hese variaions can be naure or human being. There are hree imporan reasons for invesigaing seasonal variaions. Shor erm variaions can be explained, shor erm forecasing can be possible and seasonal effecs can be disinguished from ime series. Table. Seasonal Index of Domesic Passengers of Top 15 Airpors in Turkey. Jan Feb Mar Apr May Jun Jul Aug Sep Oc Nov Dec ATATÜRK SABIHA GÖKÇEN ESENBOĞA ADNAN MENDERES ANTALYA ADANA TRABZON DİYARBAKIR MİLAS BODRUM GAZİANTEP SAMSUN ÇARŞAMBA VAN F.MELEN KAYSERİ ERZURUM DALAMAN New and innovaive projecs and sraegies should be organized o increase he capaciy of airpors including Aaürk, Sabiha Gokcen, Esenboga, Adnan Menderes and Analya Airpors for meeing esimaed demand for he nex 10 years due o Fig 1, Fig, Fig 3, Fig 4, Fig 5, Fig 6 and Fig 7. 69

6 Figure 1. Toal Domesic Passengers of Top 15 Airpors in Turkey beween Jan-008 and June-013. Table 3. Seasonal Index of Inernaional Passengers of Top 15 Airpors in Turkey. Jan Feb Mar Apr May Jun Jul Aug Sep Oc Nov Dec ATATÜRK ANTALYA SABIHA GÖKÇEN DALAMAN ADNAN MENDERES MİLAS BODRUM ESENBOĞA ADANA KAYSERİ GAZİANTEP HATAY SAMSUN ÇARŞAMBA TRABZON KONYA NEVŞEHİR-KAPADOKYA

7 Figure. Toal Inernaional Passengers of Top 15 Airpors in Turkey beween Jan-008 and June-013. Table 4. Seasonal Index of Domesic Cargo of Top 15 Airpors in Turkey. Jan Feb Mar Apr May Jun Jul Aug Sep Oc Nov Dec ATATÜRK ANTALYA A.MENDERES SABIHA GÖKÇEN ESENBOĞA ADANA TRABZON DİYARBAKIR MİLAS-BODRUM GAZİANTEP KAYSERİ VAN F.MELEN SAMSUN ÇARŞAMBA DALAMAN ERZURUM

8 Figure 3. Toal Domesic Cargo of Top 15 Airpors in Turkey beween Jan-008 and June-013 (Uni: Ton). Table 5. Seasonal Index of Inernaional Cargo of Top 15 Airpors in Turkey. Jan Feb Mar Apr May Jun Jul Aug Sep Oc Nov Dec ATATÜRK ANTALYA SABIHA GÖKÇEN DALAMAN ADNAN MENDERES ESENBOĞA MİLAS-BODRUM TEKİRDAĞ/ ÇORLU ADANA KAYSERİ GAZİANTEP TRABZON SAMSUN ÇARŞAMBA KONYA BURSA-YENİŞEHIR

9 Figure 4. Toal Inernaional Cargo of Top 15 Airpors in Turkey beween Jan-008 and June-013 (Uni: Ton). 4. FORECASTING Smoohing mehods have good shor-erm accuracy. Also heir simpliciy is one of he oher advanages. Large amoun of hisorical daa are no required. However in smoohing mehods choosing smoohing coefficien (α and/or γ) properly is very imporan. I affecs he qualiy of forecasing. For deermining hese coefficiens Excel Solver ool is used. The daa in his sudy is more convenien o curve esimaion ool of SPSS 13 package program. For mehod selecion process average squares of residuals are used. Mehods wih minimum average squares of residuals are seleced for boh curve esimaion and smoohing. In curve esimaion, for all hree variables (Passenger, Fligh, Freigh ) cubic curve esimaion mehods are seleced for forecasing. In Appendix 1, deails of mehod selecion process can be seen for all variables. For insance, in his able (Appendix 1A) minimum error square of passenger raffic variable is 4,905,51,5,046 (cubic curve esimaion s average squares of residuals). Cubic curve esimaion mehod also was seleced for Fligh and Freigh variables. In smoohing mehods, Hol s Linear Exponenial Smoohing Mehod wih Two Parameer mehod is seleced for Passenger variable, Brown s Linear Exponenial Smoohing Mehod wih Single Parameer mehod is seleced for Fligh and Linear Moving Averages mehod is seleced for Freigh. Air ranspor is he mos imporan medium for long disance ranspor of passengers and freighs and has sraegic significance for global accessibiliy [6]. The saisics already presened show ha he las 10 years (00-01) has seen significan developmen occur in he airline indusry. This increase in domesic and inernaional raffic may be due o eiher falling prices in all produc classes or increase number of airpors/ airplane firms ec. Aviaion secor in Turkey has shown a remendous growh in air ravel demand and in he number of flighs in las decade ha can be seen in Table 6, Table 8 and Table

10 Table 6. Domesic and Inernaional Passenger Esimaion in Turkey (Curve Esimaion: Cubic). Passenger Saisics in All Airpors of Turkey during Passenger Esimaions in All Airpors of Turkey for Year Passenger Passenger (Domesic) Passenger (Inernaional) 00 33,783,89 8,79,79 5,054, ,443,655 9,147,439 5,96, ,057,371 14,460,864 30,596, ,57,46 0,59,469 35,04, ,655,659 8,774,857 3,880, ,96,53 31,949,341 38,347, ,438,89 35,83,776 43,605, ,508,508 41,6,959 44,81, ,800,39 50,575,46 5,4, ,60,469 58,58,34 59,36, ,351,60 64,71,316 65,630, ,773,33 73,1,450 75,650, ,67,019 81,78,874 86,889, ,071,88 90,967, ,104, ,19, ,693,66 115,499, ,57, ,979, ,78, ,488,585 11,845,14 153,643, ,106,00 133,307,58 176,798, ,33, ,385,313 0,947, ,388, ,096,730 3,9, ,497, ,460,158 65,036, ,878,73 185,493,91 301,384,811 Figure 5. Domesic and Inernaional Passenger Esimaion in Turkey (Curve Esimaion: Cubic). 74

11 Table 7. Domesic and Inernaional Passenger Esimaion in Turkey (Hol s Linear Exponenial Smoohing Mehod wih Two Parameer). Year Passenger Passenger (Domesic) Passenger (Inernaional) Passenger Saisics in All Airpors of Turkey during Passenger Esimaions in All Airpors of Turkey for ,783,89 8,79,79 5,054, ,443,655 9,147,439 5,96, ,057,371 14,460,864 30,596, ,57,46 0,59,469 35,04, ,655,659 8,774,857 3,880, ,96,53 31,949,341 38,347, ,438,89 35,83,776 43,605, ,508,508 41,6,959 44,81, ,800,39 50,575,46 5,4, ,60,469 58,58,34 59,36, ,351,60 64,71,316 65,630, ,708,11 71,671,5 7,036, ,043,73 78,608,988 78,434, ,379,344 85,546,75 84,83, ,714,956 9,484,46 91,30, ,050,567 99,4,198 97,68, ,386, ,359, ,06, ,71, ,97,67 110,44, ,057,40 10,35, ,81, ,393,014 17,173,145 13,19, ,78,65 134,110,88 19,617, ,064,37 141,048, ,015,619 Figure 6. Domesic and Inernaional Passenger Esimaion in Turkey (Hol s Linear Exponenial Smoohing Mehod wih Two Parameer). 75

12 Table 8. Domesic and Inernaional Fligh Esimaion in Turkey (Curve Esimaion: Cubic). Fligh Saisics in All Airpors of Turkey during Fligh Esimaions in All Airpors of Turkey for Year Fligh Fligh (Domesic) Fligh (Inernaional) , ,953 18, , ,58 18, , ,07 53, ,980 65,113 86, , ,6 86, , ,177 33, , , , , ,4 369, , ,86 41, ,04, ,488 46, ,093, ,818 49, ,06, ,09 541, ,313,183 73,08 590, ,45,177 78,6 64, ,54,706 84, , ,665, , , ,794, ,396 87, ,99,800 1,031, ,390 00,070,766 1,096, ,31 01,17,915 1,16,458 1,055,458 0,371,377 1,9,350 1,14,07 03,531,8 1,97,06 1,34,0 Figure 7. Domesic and Inernaional Fligh Esimaion in Turkey (Curve Esimaion: Cubic). 76

13 Table 9. Domesic and Inernaional Fligh Esimaion in Turkey (Brown s Linear Exponenial Smoohing Mehod wih Single Parameer). Year Fligh Fligh (Domesic) Fligh (Inernaional) Fligh Saisics in All Airpors of Turkey during Fligh Esimaions in All Airpors of Turkey for , ,953 18, , ,58 18, , ,07 53, ,980 65,113 86, , ,6 86, , ,177 33, , , , , ,4 369, , ,86 41, ,04, ,488 46, ,093, ,818 49, ,145,173 63,353 51, ,197,91 645,88 551, ,49, , , ,301,58 690, , ,353, , , ,405, , , ,457, ,55 699, ,510,00 781,054 78, ,56,10 803, , ,614,38 86,11 788, ,666, , ,717 Figure 8. Domesic and Inernaional Fligh Esimaion in Turkey (Brown s Linear Exponenial Smoohing Mehod wih Single Parameer). 77

14 Table 10. Domesic and Inernaional Freigh Esimaion in Turkey (Curve Esimaion: Cubic). Freigh Saisics in All Airpors of Turkey during Freigh Esimaions in All Airpors of Turkey for Year Freigh Freigh (Domesic) Freigh (Inernaional) , ,6 715, , , , ,164,349 6, , ,304,41 34, , ,360, ,06 971, ,546, ,94 1,131, ,644,014 44,555 1,19, ,76, ,833 1,41,51 010,01, ,710 1,466, ,49, ,834 1,631,639 01,49, ,076 1,616, ,493, ,349 1,797,36 014,681, ,44 1,931, ,878, ,391,071, ,085, ,69,17, ,300, ,767,368, ,56,49 1,000,058,56, ,76,13 1,073,007,689, ,008,68 1,151,056,857, ,66,313 1,34,644 3,031, ,535,401 1,34,15 3,11, ,816,331 1,40,08 3,396,1 Figure 9. Domesic and Inernaional Freigh Esimaion in Turkey (Curve Esimaion: Cubic). 78

15 Table 11. Domesic and Inernaional Freigh Esimaion in Turkey (Linear Moving Averages). Year Freigh Freigh (Domesic) Freigh (Inernaional) Freigh Saisics in All Airpors of Turkey during Freigh Esimaions in All Airpors of Turkey for , ,6 715, , , , ,164,349 6, , ,304,41 34, , ,360, ,06 971, ,546, ,94 1,131, ,644,014 44,555 1,19, ,76, ,833 1,41,51 010,01, ,710 1,466, ,49, ,834 1,631,639 01,49, ,076 1,616, ,540,14 710,710 1,89, ,73,57 765,18 1,958, ,907,01 819,547,087, ,090, ,965,16, ,73,918 98,383,345, ,457,366 98,80,474, ,640,814 1,037,0,603, ,84,63 1,091,638,73, ,007,711 1,146,057,861, ,191,159 1,00,475,990, ,374,608 1,54,893 3,119,715 Figure 10. Domesic and Inernaional Freigh Esimaion in Turkey (Linear Moving Averages). 79

16 5. CONCLUSION AND SUGGESTIONS Forecasing echniques are imporan ools in operaional managemen for creaing realisic expecaions. In lieraure many differen echniques in he area of saisics and arificial inelligence were proposed for achieving close esimaions. In his sudy, cubic curve esimaion mehod is seleced for forecasing Passenger, Fligh and Freigh variables. The reason of his is cubic curve esimaion mehod has higher order polynomial funcion han oher curve fiing mehods. Therefore i has more coefficiens and his decreases he average squares of residuals. Also in smoohing mehods, Hol s Linear Exponenial Smoohing Mehod wih Two Parameer is seleced for Passenger variable, Brown s Linear Exponenial Smoohing Mehod wih Single Parameer is seleced for Fligh variable and Linear Moving Averages mehod is seleced for Freigh variable. Aviaion secor in Turkey has shown a remendous growh in air ravel demand and in he number of flighs in las decade. Airpor planning includes capaciy, local and global planning, aviaion raffic forecasing, and airspace planning. One of he imporan saisical ools of capaciy planning is obaining seasonal indexes of all airpors. For insance Milas Bodrum Airpor has inernaional passenger seasonal indexes of 1.8 for March and 54.3 for Augus. These seasonal airpors can be effecive when hey maximize heir produciviy wih accurae capaciy planning using quaniaive echniques. The seasonal index can also be used o derive an improved, seasonally adjused forecas for logisic demands. Wih Aaurk Airpor and Sabiha Gokcen Airpor Isanbul is one of he mos imporan air hub ciies in he world. Also hird airpor of Isanbul will be consruced including six runways, 16 axiways, 88 passenger bridges, 165 aircraf passenger bridges a all erminals and a 6.5 million-square-meer apron wih capaciy for 500 aircraf.. Once all six of he planned runways are complee, he capaciy is expeced o increase o 150 million passengers, one of he world s larges in erms of he passenger capaciy a full capaciy. When we check he forecasing numbers he hird airpor is necessary for Isanbul. 6. REFERENCES [1] Grach, H.A. and Darkow, I.L., (010). Scenarios for he logisics services indusry: A Delphibased analysis for 05, In. J. Producion Economics 17, [] Charles, M.B., Barnes, P., Ryanb, N. and Clayon, J., (007). Airpor fuures: Towards a criique of he aeroropolis model, Fuures 39, [3] Carson, R.T., Cenesizoglu, T. and Parker, R., (011).Forecasing (aggregae) demand for US commercial air ravel, Inernaional Journal of Forecasing 7, [4] China,A.T.H., Tay, J.H., (001). Developmens in air ranspor: implicaions on invesmen decisions, profiabiliy and survival of Asian airlines, Journal of Air Transpor Managemen 7, [5] Adrangi, B., Charah, A. and Raffiee, K., (001). The demand of US air ranspor service: a chaos and nonlineariy invesigaion, Transporaion Research, Par E, 37, [6] Jonga, G., Gunnc, H. and Akiva, M.B., (004). A mea-model for passenger and freigh ranspor in Europe Transpor Policy 11, [7] Masumoo, H., (004). Inernaional urban sysems and air passenger and cargo flows: some calculaions, Journal of Air Transpor Managemen 10, [8] Lee, H. S., (009). The neworkabiliy of ciies in he inernaional air passenger flows Journal of Transpor Geography 17, [9] Hui, G W. L., Hui, Y. V. and Zhang, A., (004). Analyzing China s air cargo flows and daa. Journal of Air Transpor Managemen 10, [10] Hwang, C. C., Shiao, G. C., (011). Analyzing air cargo flows of inernaional roues: an empirical sudy of Taiwan Taoyuan Inernaional Airpor. Journal of Transpor Geography 19, [11] Mason, K.J., (005). Observaions of fundamenal changes in he demand for aviaion services. Journal of Air Transpor Managemen 1, 19 5 [1] Mahiessen, C.W., (004). Inernaional air raffic in he Balic Sea Area: Hub-gaeway saus and prospecs. Copenhagen in focus. Journal of Transpor Geography 1, [13] Sengupa, P., Tandale, M., Cheng, V., Menon, P., (011).Air Esimaion and Decision Suppor for Sochasic Flow Managemen, American Insiue of Aeronauics and Asronauics Guidance, Navigaion, and Conrol Conference, 8-11 Augus 011, Porland, Oregon [14] Önder, E., Hasgül, O., 009. Time Series Analysis wih Using Box Jenkins Models and Arificial Neural Nework for Forecasing Number of Foreign Visiors. Journal of Insiue of Business Adminisraion - Yöneim (0), 6, 6-83 [15] Orhunbilge, N., 1999, Time Series Analysis, Forecasing and Price Index. Isanbul Universiy, School of Business Press, Publicaion No: 77, (In Turkish) 80

17 [16] ( ) VITAE Emrah ÖNDER He graduaed as an elecronic engineer from I.U. Elecronic Engineering Deparmen, and received a MSc and PhD degree from he I.U. School of Business, Deparmen of Quaniaive Mehods. He also received MBA diploma from Ball Sae Universiy, Indiana/USA. He is currenly a research and eaching assisan of I.U. School of Business. His dominan scienific ineres focuses on: quaniaive mehods. Sulan KUZU She graduaed from Anadolu Universiy, Business Faculy and received a BSc and MSc in Mahemaics Teacher Educaion in Marmara Universiy, Aaurk Educaion Faculy. She is currenly a research and eaching assisan and PhD suden of I.U. School of Business. Her dominan scienific ineres focuses on: saisics. 81

18 APPENDIX 1 A. Model selecion using average squares of residuals (Passenger ) Mehod Parameers Average (e ) Selecion Linear Consan 16,060, β 1 9,694, β β 3 3,45,605,105,80 Logarihmic Consan 11,73, β 1 39,78, β β 3 184,449,05,03,090 Inverse Consan 98,004, β 1-86,599, β β 3 466,148,83,099,064 Quadraic Consan 8,40, β 1 3,998, β 474, β 3 5,671,615,054, Curve Esimaion Cubic Consan 4,369, β 1 7,330, β -190, β ,905,51,5,046 Seleced Compound Consan 9,47, β β β 3 8,583,577,33,59 Power Consan 6,5, β β β 3 84,896,370,558,36 S Consan β β β 3 384,538,387,801,016 Growh Consan β β β 3 8,583,577,33,59 Exponenial Consan 9,47, β β β 3 8,583,577,33,59 Single Moving Averages 446,755,763,0,740 Brown s Simple Exponenial Smoohing Mehod 0.010,695,38,614,09,580 Linear Moving Averages 7,637,885,504,08. Smoohing Brown s Linear Exponenial Smoohing Mehod wih Single Parameer ,574,775,683,477 Hol s Linear Exponenial Smoohing Mehod wih Two Parameer ,844,8,909,517 Seleced Brown s Quadraic Exponenial Smoohing Mehod ,610,613,734,751 8

19 APPENDIX 1 B. Model selecion using average squares of residuals (Fligh ) Mehod Parameers Average (e ) Selecion Linear Consan 45, β 1 74, β β 3 993,580,0 Logarihmic Consan 06, β 1 307, β β 3 9,450,003,643 Inverse Consan 883, β 1-684, β β 3 6,193,439,739 Quadraic Consan 304, β 1 48, β, β 3 599,010,34 1. Curve Esimaion Cubic Consan 301, β 1 49, β 1, β ,748,63 Seleced Compound Consan 331, β β β 3 964,87,8 Power Consan 301, β β β 3 4,587,184,376 S Consan β β β 3 1,645,856,879 Growh Consan β β β 3 964,87,8 Exponenial Consan 331, β β β 3 964,87,8 Single Moving Averages 6,465,530,814 Brown s Simple Exponenial Smoohing Mehod ,461,36,04 Linear Moving Averages,531,5,630. Smoohing Brown s Linear Exponenial Smoohing Mehod wih Single Parameer 0.990,7,454,50 Seleced Hol s Linear Exponenial Smoohing Mehod wih Two Parameer ,51,419,185 Brown s Quadraic Exponenial Smoohing Mehod 0.4,908,780,83 83

20 APPENDIX 1 C. Model selecion using average squares of residuals (Freigh ) Mehod Parameers Average (e ) Selecion Linear Consan 705, β 1 141, β β 3 3,791,439,16 Logarihmic Consan 60, β 1 588,64.09 β β 3 30,050,753,944 Inverse Consan 1,93, β 1-1,336, β β 3 86,568,675,890 Quadraic Consan 784, β 1 105, β 3, β 3 3,075,499, Curve Esimaion Cubic Consan 777, β 1 111,65.56 β 1, β ,073,180,63 Seleced Compound Consan 845, β β β 3 4,61,86,95 Power Consan 777,44.30 β β β 3 15,961,066,1 S Consan β β β 3 71,889,35,380 Growh Consan β β β 3 4,61,86,95 Exponenial Consan 845, β β β 3 4,61,86,95 Single Moving Averages 90,51,0,919 Brown s Simple Exponenial Smoohing Mehod ,080,67,793 Linear Moving Averages (k=3) 10,478,903,14 Seleced. Smoohing Brown s Linear Exponenial Smoohing Mehod wih Single Parameer ,176,570,816 Hol s Linear Exponenial Smoohing Mehod wih Two Parameer ,8,609,810 Brown s Quadraic Exponenial Smoohing Mehod ,468,59,780 84

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