Air Traffic at Three Swiss Airports: Application of Stamp in Forecasting Future Trends

Air Traffic at Three Swiss Airports: Application of Stamp in Forecasting Future Trends



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.


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.


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

lowercase y subscript {lowercase t} = (column 1 row 1 lowercase m subscript {lowercase t} column 1 row 2 lowercase p subscript {lowercase t},

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 Zrich 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.


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.


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 Aroport International de Genve), Valrie Meny (Statistical Department of EuroAirport), and Merk Jrg (Stab/Statistik Bundesamt fr 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.


EuroAirport. 2004. Face Une Situation conomique Perturbe et la Chute de Son Trafic, l'EuroAirport s'Adapte aux Nouveaux Besoins du March et Affirme sa Volont de Renouer avec la Croissance en 2004.

______. 2005. Evolution Positive du Traffic l'EuroAirport: Innovation et Adaption Russie aux Nouveaux Besoins du March. 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 Zrcher Zeitung. Zrich, Switzerland.


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},

t = 1, ., T      (4)

where λc is the frequency, in radians, in the range 0 < λc < 1, κt, and lowercae kappa asterisk subscript {lowercase t - 1}, are two mutually uncorrelated white noise disturbances with zero means and common variance lowercase sigma superscript {2} subscript {lowercase kappa}, 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

uppercase e (lowercase kappa subscript {lowercase t} lowercase kappa asterisk prime subscript {lowercase t} = 0,  lowercase t = 1, ..., uppercase t     (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 uppercase i subscript {lowercase t subscript {lowercase a lowercase o}} has the following form:

uppercase i subscript {lowercase t subscript {lowercase a lowercase o}} = {1 if lowercase t = t subscript {lowercase a lowercase o}, 0 if lowercase t is not equal to lowercase t subscript {lowercase a lowercase o}        lowercase t = 1, ..., uppercase t

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 uppercase i subscript {lowercase t subscript {uppercase l uppercase s}} has the following form:

uppercase i subscript {lowercase t subscript {uppercase l uppercase s}} = 0 if lowercase t is less than lowercase t subscript {uppercase l uppercase s}, 1 if lowercase t is greater than or equal to lowercase t subscript {uppercase l uppercase s}        lowercase t = 1, ..., uppercase t


Table A-1 illustrates the nature of the outputs used in the main text. The figures are taken from table 1 in the text.


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.


1. See appendix 1 for the definition of the intervention variables.


1 Corresponding author: M. Scaglione, Institute for Economics & Tourism, University of Applied Sciences Valais, TECHNO-Ple Sierre 3, CH 3960 Sierre, Switzerland. E-mail:

2 A. Mungall, Ecole Htelire de Lausanne, Le Chalet--Gobet, CH - 1000 Lausanne 25, Switzerland. E-mail: