Air Traffic at Three Swiss Airports: Application of Stamp
in Forecasting Future Trends
MIRIAM SCAGLIONE 1,
* ANDREW MUNGALL 2
ABSTRACT
This paper presents forecasting trends for numbers of air
passengers and aircraft movements at the three main airports in
Switzerland: Zurich, Geneva, and Basel. The case of Swiss airports
is particularly interesting, because air traffic was affected in the
recent past not only by the September 11, 2001, terrorist attacks
but also by the bankruptcy of the national carrier, Swissair, that
same year. A structural time series model (STS) is created using
Stamp software to facilitate forecasting. Results, based on
readily available data (i.e., passengers and movements), show that
STS models yield good forecasts even in a relatively long run of
four years.
KEYWORDS: Structural time series, forecast, airports,
Switzerland, air traffic.
INTRODUCTION
Airports are now widely recognized as having a considerable
economic and social impact on their surrounding regions. These
impacts go far beyond the direct effect of an airport's operation on
its neighbors and extend to the wider benefits that access to air
transport brings to regional business interests and consumers.
The economic benefits of air transport may be assessed by looking
at the full extent of the industry's impact on the overall economy,
from the movement of passengers and cargo to the economic growth
that the industry's presence stimulates in a local area.
In this respect, Switzerland represents an interesting case.
First, half of the earnings of the Swiss economy come from abroad.
Fast, direct access to the different markets around the world is
therefore very important, especially when Switzerland's dependence
on exports will increase in the future. In this economy, the
industry with the highest share of exports is metallurgy and
mechanical engineering. Around 75% of its production is exported. In
the Swiss tourism industry, exports represented by the expenses of
foreign tourists are also important. Of a total tourism revenue of
22.2 billion Swiss francs (CHF) in 2003 (Swiss Federal Statistical
Office 2004), 12.6 billion CHF (60% of the amount) came from foreign
tourists.
Second, Swiss air transport has recently been facing rapid
change. During the last half of the 1990s, Swiss airports revisited
their respective strategies following the decision made by the
national carrier, Swissair, in 1996 to concentrate all long-haul
flights at Zurich-Unique Airport (ZRH). Also at this time, the
Basel/Mulhouse Airport (BSL) made plans to become a European hub or
a spoke for Swissair, and, therefore, decided on significant
expansion investments. This obliged Geneva International Airport
(GVA) to adopt an open-sky policy, where foreign air carriers could
benefit from so-called "fifth-freedom" rights, enabling them to
provide intercontinental services to and from Geneva. The Swissair
bankruptcy in 2001 changed the context, calling the expansion policy
of ZRH airport into question.
This study uses the data from the three main Swiss airports-ZRH,
GVA, and BSL-to show the overcapacity of two of the three by
forecasting these series to 2006. The average share of overall
aircraft movements at the three airports was: 46% (±5), 32% (±3),
and 22% (±3); for passengers, the share was 59% (±5), 32% (±4), and
9% (±3), respectively.
The structure of the paper is as follows: the next section
describes the data used for this analysis, then we provide the
forecasts based on three models (one for each airport) to a horizon
of 2006. All sections use structural time series (STS) models and
the Stamp software for STS (Koopman et al. 2000). The last
section provides conclusions based on these results.
DATA
For our analysis, we obtained data from the statistical
department of each airport studied. Each provided yearly
observations from 1949 to 2003, except for GVA, whose data began in
1922. We considered two principal indicators: air movements and
passengers.
Traffic Forecasts
We built bivariate models for each airport using the vector of
variables
,
where mt denoted the number of movements
for a given airport, and pt denoted the
number of passengers. The choice of the bivariate model seems
appropriate, because aircraft and passengers belong to the same
economic system and this kind of model allows for interaction
between the two variables. These models are called Seemingly
Unrelated Time Series Equations (SUTSE) and are an extension of
univariate forms, with the advantage of allowing for
cross-correlation leads between variables. In Stamp, SUTSE
are particularly appealing because, on the one hand, models with
common factors emerge as a special case; on the other, the direct
analysis of the unobservable components provides a more efficient
forecast and inference (see appendix 1 for details). In this study,
the variables are transformed to logarithms so that the model is
multiplicative. Such a transformation allows for percentage changes
rather than absolute changes in traffic levels and also helps to
stabilize the variances of the variables.
Analysis for GVA
For GVA, while annual data are available from 1922, the first
major facility was built in 1949. Given that the period 1949 to 1952
was one of transition, we used data from 1953 to 2002. The
observation for 2003 was used to evaluate the probability of a
structural break using the post-predictive features of Stamp
(Koopman et al. 2000, pp. 39-40).
Table
1 shows the hyper-parameters of the model (table A1 in the
appendix provides an interpretation of these values). Table
2 shows statistics tests normally used to evaluate the
goodness-of-fit of the model. In the case of GVA, only the Box-Ljung
(test of residual serial correlation) statistic is slightly
significant (p-value = 0.08) for passengers. The model is a
local linear trend and a common cycle (table
3).
Table 1 also provides the list of intervention variables.1
There is no intervention for passenger series, but there are two
interventions in the aircraft movement component. The first occurs
in 1956 and is a positive level shift, probably explained by the
increase of movements owing to the start of the jet aircraft era.
The outlier intervention (AO) in 1967 is difficult to explain;
however, we retained it in the model for consistency.
The analysis of the components obtained in the STS modeling
(i.e., trend, slopes, and cycles) highlights some interesting
features of the phenomena under study. Figure
1 shows some of the components of the models. First, the slopes
are parallel in logarithms, suggesting that the rates of growth,
though different, have a parallel evolution. In statistical terms,
it means that the system composed of the passengers and movements is
co-integrated to an order of (2,2) and there is a combination that
is stationary (see Koopman et al. 2000, p. 86; Song and Witt 2000,
p. 56). As the data are in logarithms, this component represents the
rate of growth and can be read as tracking its acceleration and
deceleration.
The growth rates gradually declined from the mid-1950s to the
mid-1970s and then stabilized at about 3% for passengers and 1% for
movements (see the last column in table 3). This difference in rates
clearly reflects the increase in the jet aircraft era. The mid-1950s
brought the prospect of commercial jet airliners in the near future,
with all it would entail in terms of longer runways and greater
terminal capacity. The Swiss and French authorities reached an
agreement concerning an exchange of land with France. Provision was
also made for a sector of the future terminal to become a "French
Airport," linked to Ferney-Voltaire in France by an
extra-territorial connection. The agreement was ratified by the
Federal Assembly in 1956 and by the French Parliament in 1958.
Other important features summarized in table 3 for GVA are the
existence of a cycle of approximately 12 years that is stochastic,
but with a correlation of 1; this means that the two cycles
(passengers and air movements) move together. The table also shows
that the amplitude of the cycle (at the end of the series) is less
than 2.5% of the trend for passengers and less than 2% for
movements. Figure
2 shows the trend and the actual values in logs with the
contribution of the cycles.
Table
4(A) shows the number of passengers forecast and observed for
2003 and 2004. The forecasts underestimate the observed figures by
about 3% for 2003 and 6% for 2004. Table
4(B) shows that aircraft movements observed and forecast are
very close for both 2003 and 2004, both approximately 1.6 hundreds
of thousands.
In spite of the slightly high error for passengers, table 4(A)
shows that the numbers observed remain inside the confidence
interval of one standard error, and therefore the model does not
need to be reviewed. In 2003, GVA outperformed the 2000 record for
passengers; this upward tendency was confirmed in 2004. This
increased passenger level can be explained by the innovative policy
carried out by the GVA authorities and the reinforcement of the
presence of low-cost carriers that have a high passenger load rate
for their flights. As an example, on April 22, 2004, the GVA Board
decided to adopt a loyalty policy for both the old and new companies
operating in the airport. Under this policy, GVA would return up to
40% of the airport taxes (excluding the share relating to security)
to all companies that signed a commitment to operate from the
airport for three to five years. At the same time, GVA decided to
segment its terminals. The principal terminal remains a conventional
one, and GVA renovated the old terminal and offered to let all
companies (even though low-cost companies suggested this measure)
use it at a lower tax level than the principal one. Table 4 (B)
shows that GVA will need more than two years to return to the
maximum level of movements registered in 2000 (1.71 hundreds of
thousands).
Figure
3 also shows the forecasts for 2004 to 2006, which indicate a
strong upward trend for passengers and a slight upward trend for
aircraft movements. Once more, this difference in the speed of
evolution between movements and passengers can be explained by the
aggressive GVA policy in trying to capture the low-cost market
(e.g., easyJet, which has an excellent aircraft occupancy
rate). Thus, with 25% of the market share of GVA traffic in 2003,
easyJet has become, for the first time, the most important
carrier in Geneva. The market share of the national airline, Swiss,
amounted only to 21.3%.
Analysis for ZRH Airport
For ZRH airport, we considered data from 1953, which coincided
with the formal inauguration of the present location (also called
Kloten Airport). During the 1980s and 1990s, the airport experienced
rapid expansion. The number of passengers reached 12 million in 1990
and 22 million in 2000. Thus, in 1995 the Zürich electorate accepted
a further expansion program for the airport, with a new terminal, a
new airside center (linking the different terminals) and underground
facilities. Initially, the expectation was to complete the expansion
by 2005, with the capacity of the airport increasing from 20 million
to 40 million passengers per year. As a consequence of the events of
2001, which form the object of this analysis, this extension phase
is being implemented more slowly and Terminal B (capacity of about 5
million passengers) has been closed down.
The model calculated on the sample data from 1953 to 2002 shows
that the observed totals for 2003 lay outside the forecast
confidence interval of one standard deviation. Therefore, the
authors reviewed the model, taking 2003 as the last observation, and
a level shift intervention in the model for 2002. Table 1 shows that
the intervention has a significant negative coefficient for both
series, passengers and movements, indicating that the shift in both
trends is decreasing. The model is a smoothed trend with a
drift.
Figure
4 shows the slope, namely the rate of growth for the series. For
movements, the range was about 5% (from 6% to 1%) and was quite
steady. For passengers, the range was about 19% (from 18% to -1%).
The figure also shows the external shocks for both series. Indeed,
the rate of growth ZRH passengers becomes negative in the same year
that Swissair went bankrupt.
Analysis for BSL Airport
The analysis of BSL airport uses observations from 1956 to 2002.
The reason for chosing 1956 is that at that time the facilities
development process was quite mature. When the airport reached 3
million passengers per year at the end of 1998, expansion seemed to
be essential and urgent. Extension work on the terminal buildings
will allow for further expansion in the number of passengers in the
future, to a capacity of 5 million per year.
The model is a local linear trend, plus a cycle, having a common
slope, which means a cointegration (2,2) for the two series. The
estimated growth rate of the fitted stochastic trend is positive for
passengers (about 2%) and negative for movements (-2%) at the end of
the sample period.
Table 4(A) shows a high error in the overestimation for
passengers in 2003, which could be due to the drastic reduction of
flights by the national carrier, Swiss (elimination of 11
destinations and 7 transfer flights since March 2003), which
strongly affected the number of transit passengers. The good
performance in the forecast of movements could be explained, in
part, by the increasing number of charters (over 3% against 2002)
following the arrival of new carriers (EuroAirport 2004).
The 2004 forecast is better for passengers than for movements,
nevertheless both forecast figures remain inside the confidence
interval of one standard deviation. On the one hand, the number of
passengers on scheduled flights increased by 8% against 2003, given
the arrival of easyJet offering four new destinations. On the
other hand, the decrease in the number of movements is explained by
the increasing load rate and the use of aircraft with larger
capacity (EuroAirport 2005). The former fact explains the apparent
contradiction of the increasing number of passengers despite a
decreasing number of movements. Finally, this high error in the
forecast suggests that Basel Airport is in a structural change phase
(i.e., the percentage of transit passengers in 2004 was 2%, whereas
in the past it was approximately 28%). Nevertheless, BSL seems to be
growing once again owing to a policy centered more on low-cost
carriers and charters and much less on its original vocation of
being a Euro-Hub.
CONCLUSION
The forecasts here show that neither ZRH nor BSL seems likely to
return to the level of the record year of 2000, either for
passengers or for aircraft movements, by 2006. The only airport that
was able to beat the record numbers achieved in 2000 was GVA, but
only in the case of passengers.
The innovative policy carried out by GVA was a good solution to
overcome the 2001 crises of the bankruptcy of Swissair and the U.S.
terrorist attacks. This being said, GVA had begun to rethink its
strategy earlier than the other two airports, owing to the decision
of the national carrier to concentrate all long-haul flights at ZRH
in 1996.
The high errors in the forecast figures for BSL are a result of
the structural changes taking place at that airport since 2003;
namely, an evolution away from being a spoke and toward becoming a
city-to-city European airport. Therefore, the analysis of those
differences could be a tool for assessing the effectiveness of the
measures undertaken by BSL. In fact, table 4(A) shows that a
slightly decreasing trend was forecast for passengers between 2003
and 2004, whereas the observed figures show the opposite. This may
be due, at least in part, to the success of the new policy adopted
by the Board of BSL.
Finally, the use of Stamp software on the series of
passengers and movements through a SUTSE model appears to be an
interesting tool for forecasting air transportation data. On the one
hand, the forecasts are good if there are no structural changes (as
in the case of BSL); on the other hand, analysis of the components
(i.e., trends, slopes, and cycles) gives a good insight into the
dynamic of the series. Moreover, the data used (i.e., passengers and
movements) are easily available.
ACKNOWLEDGMENTS
The authors wish to thank the following individuals for their
invaluable support: Merrick Fall (EHL), Regula Catsantonis (Unique
Airport Verkehrsdaten/Statistik), Robert Weber (Statistical
Department of Aéroport International de Genève), Valérie Meny
(Statistical Department of EuroAirport), and Merk Jürg
(Stab/Statistik Bundesamt für Zivilluftfahrt). Thanks also go to
Professor Andrew Harvey (Cambridge University) and to the anonymous
referees for their helpful comments on the earlier version of this
study.
REFERENCES
EuroAirport. 2004. Face à Une Situation Économique
Perturbée et à la Chute de Son Trafic, l'EuroAirport s'Adapte aux
Nouveaux Besoins du Marché et Affirme sa Volonté de Renouer avec la
Croissance en 2004.
______. 2005. Evolution Positive du Traffic à
l'EuroAirport: Innovation et Adaption Réussie aux Nouveaux Besoins
du Marché. En 2005: Retour de la Croissance.
Harvey, A.C. 1990. Forecasting, Structural Time
Models, and the Kalman Filter. Cambridge, UK: Cambridge
University Press.
Koopman, S.J., A.C. Harvey, J.A. Doornik, and N.
Shepard. 2000. Stamp: Structural Time Series Analyser, Modeller
and Predictor. London, England: Timberlake Consultants, Ltd.
Song, H. and S.F. Witt. 2000. Tourism Demand
Modeling and Forecasting. Amsterdam, The Netherlands:
Pergamon.
Swiss Federal Statistical Office. 2004. Annuaire
Statistique de la Suisse. Edited by Neue Zürcher Zeitung.
Zürich, Switzerland.
APPENDIX
The structural time series model aims to capture the salient
characteristics of stochastic phenomena, usually in the form of
trends, seasonal or other irregular components, explanatory
variables, and intervention variables. This model can reveal the
components of a series that would otherwise be unobserved, greatly
contributing to thorough comprehension of the phenomena. We describe
here only the elements necessary for this study; for a complete
description see Harvey (1990) and Koopman et al. (2000). An STS
multivariate model may be specified as:
Observed variables = trend +
cycle + intervention + irregular
The algebraic form for the N series is:
y t = μ t +
ψ t + Λ I t +
ε t
ε t ~ NID (0,
Σ2ε)
t = 1, .,
T (1)
Unless otherwise stated, the elements in equation (1) are
(N x 1) vectors,
where yt = the vector of observed
variables,
μt = the stochastic trend,
ψt = the cycle,
Λ = the N x K* matrix
of coefficients for the interventions, and
It= the K* ×
1 vector of interventions.
The stochastic trend is intended to capture the long-trend
movements in the series and trends other than linear ones, and is
composed of two elements: the level (2) and the slope (3). The trend
described below allows the model to handle these.
μ t = μ t -
1 + β t - 1 + η
t
η t ~ NID (0,
Σ2η)
t = 1, .,
T (2)
β t = β t -
1 + ς t
ς t ~ NID (0,
Σ2ς)
t = 1, .,
T (3)
If the variances of the irregular components
εt in (1), the disturbances of the
level ηt in (2), and at least one of
the slope terms ζt are simultaneously
strictly positive, the model is a local linear trend.
When the level component is fixed and different from zero, and
when the two other variances are not zero, the model is called a
"smoothed trend with a drift."
For a univariate model, the cycle
ψt has the following statistical
specification:
![[column 1 row 1 lowercase psi subscript {lowercase t} column 1 row 2 lowercase psi asterisk subscript {lowercase t} = lowercase rho [column 1 row 1 cosine lowercase lambda subscript {lowercase c} column 1 row 2 negative sine lowercase lambda subscript {lowercase lambda lowercase c} column 2 row 1 sine lowercase lambda subscript {lowercase c} column 2 row 2 cosine lowercase lambda subscript {lowercase c}] [column 1 row 1 lowercase psi subscript {lowercase t minus 1} column 1 row 2 lowercase psi asterisk subscript {lowercase t minus 1} plus [column 1 row 1 lowercase kappa subscript {lowercase t} column 1 row 2 lowercase kappa subscript {lowercase t minus 1},](https://webarchive.library.unt.edu/eot2008/20090115201042im_/https://www.bts.gov/publications/journal_of_transportation_and_statistics/volume_08_number_01/images/Scaglione-30.gif)
t = 1, .,
T (4)
where λc is the frequency, in radians,
in the range 0 < λc < 1,
κt, and , are two mutually uncorrelated white noise
disturbances with zero means and common variance , and ρ is the damping factor. The
period of the cycle is 2π / λc.
Cycles can also be introduced into a multivariate model. The
disturbances may be correlated; the same, incidentally, can occur
with any components in multivariate models. Because the cycle in
each series is driven by two disturbances, there are two sets of
disturbances and Stamp assumes that they have the same
variance matrix (Koopman et al. 2000, p. 76), that is:
![uppercase e (lowercase kappa subscript {lowercase t} lowercase kappa prime subscript {lowercase t} = uppercase e (lowercase kappa subscript {lowercase t} asterisk lowercase kappa subscript {lowercase t} asterisk prime) = uppercase sigma subscript lowercase kappa](https://webarchive.library.unt.edu/eot2008/20090115201042im_/https://www.bts.gov/publications/journal_of_transportation_and_statistics/volume_08_number_01/images/Scaglione-38.gif)
(5)
where Σk is a N × N
variance matrix.
Stamp has pre-programmed the following exogenous
intervention variables used in this study:
1. AO: it is an unusually large value of the irregular
disturbance at a particular time. It can be captured by an
impulse intervention variable that takes the value of the
outliers as one at that particular time, and zero elsewhere. If
tao is the time of the outlier, then the
exogenous intervention variable has the following form:
![lowercase t = 1, ..., uppercase t](https://webarchive.library.unt.edu/eot2008/20090115201042im_/https://www.bts.gov/publications/journal_of_transportation_and_statistics/volume_08_number_01/images/Scaglione-45.gif)
2. LS: this kind of intervention handles a structural
break in which the level of the series shifts up or down. It is
modeled by a step intervention variable that is zero before
the event and one after it. If tLS is the
time of the level shift, then the exogenous intervention variable
has the following form:
![lowercase t = 1, ..., uppercase t](https://webarchive.library.unt.edu/eot2008/20090115201042im_/https://www.bts.gov/publications/journal_of_transportation_and_statistics/volume_08_number_01/images/Scaglione-45.gif)
Output
Table
A-1 illustrates the nature of the outputs used in the main text.
The figures are taken from table 1 in the text.
Diagnostics
The diagnosis test statistics for a single series in an STS model
are the following (see Koopman 2000, pp. 182-183):
- Normality test: the Doornik-Hansen statistic, which is the
Bowman-Shenton statistic with the correction of Doornik and
Hansen. Under the null hypothesis that the residuals are normally
distributed, the 5% critical value is approximately 6.0.
- Heteroskedasticity test: A two-sided F-test that
compares the residual sums of squares for the first and last
thirds of the residuals series.
- DW: The Durbin-Watson statistic for residual autocorrelation;
under the null hypothesis, it is distributed approximately as
N(0,1/T), T being the number of observations.
- Box-Ljung Q-statistic: A test of residual serial
correlation, based on the first P residual autocorrelations
and distributed as chi-square, with P-n+1 df, when
n parameters are estimated.
END NOTE
1. See appendix 1 for the definition of
the intervention variables.
ADDRESSES FOR CORRESPONDENCE
1 Corresponding
author: M. Scaglione, Institute for Economics & Tourism,
University of Applied Sciences Valais, TECHNO-Pôle Sierre 3, CH 3960
Sierre, Switzerland. E-mail: miriam.scaglione@hevs.ch.
2 A. Mungall, Ecole
Hôtelière de Lausanne, Le Chalet-à-Gobet, CH - 1000 Lausanne 25,
Switzerland. E-mail: Andrew.Mungall@ehl.ch.
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