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
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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
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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.
yt1 
yt1 
yt1 
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   ) yt1
(26)
yt  yt 1   ( yt 1  yt1 )
(27)
yt  yt1   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  yt1  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    yt1  bt 1 
(39)
bt    yt  yt1   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    yt1
(42)
yt   yt  1    yt1
(43)
yt   yt  1    yt1
(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    yt1
(34)
yt   yt  1    yt1
(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.
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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
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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–
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[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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forecasting air traffic volumes using smoothing techniques