Demand forecasting is a crucial firststep in planning Brazils civil aviationsystem (Sistema de Aviao Civil,SAC). Such planning underlies thewhole endeavour to develop the infra-structure necessary to meet demand.Underestimated forecasts will lead toSAC congestion, and thus to inefficien-cy and high operating costs. In addition,users (passengers, airlines etc.) willperceive low levels of service. On theother hand, if forecasts are overestimat-ed there will be surplus capacity in theSAC, generating additional asset main-tenance costs. In that case, users and thegeneral public have to defray the costsof idle capacity, which is not a healthysituation given the limitations oninvestment funding. Airport price man-agement in congested conditions isaddressed in considerable detail in theliterature. Such management canreduce the impact of inadequate infra-structure. However, one of the func-tions of planning is to avoid congestion,so as to ensure appropriate service lev-els and to direct investment efficiently.In Brazil, where nearly all airport infra-structure connected with regular pas-senger transport is managed by a publicenterprise, it is fundamentally impor-tant to optimize infrastructure in orderfor the SAC to evolve. For that purpose,demand forecasting is fundamental tothe planning process.

This paper aims to discuss the processof estimating overall demand for pas-senger kilometres in regular domesticair transport in Brazil. Although disag-gregated forecasts for each airport aremore useful for planning capacity, the

aggregate forecast for the SAC as awhole is a valuable indicator of theplanning process and helps delimit thedisaggregated models of futuredemand. The aggregate forecast isupdated periodically by the CivilAviation Department (Departamentode Aviao Civil, DAC), attached to theMinistry of Defence, which at presentforms the basis for the recently-createdNational Civil Aviation Agency(Agncia Nacional de Aviao Civil,ANAC), whose role is to regulate thesector.

The methodology currently usedinvolves a complex set of hypotheseson evolution of Brazils GDP anddomestic passenger yield (YPD),besides using a dummy variable inorder to absorb contingent effects in theeconomy. Although the dummy vari-able is used in connection with anexplanation of an economic crisis thatoccurred from 1991 to 1992, it can beargued that this realignment forms partof a cycle proper to the sector. In addi-tion, the uncertainty of the forecast isgreatly increased by the various uncer-tainties involved in forecasting theexplanatory variables of the economet-ric model. By contrast, the observedhistorical series signals the possibilityof a simple time series approach thatcould be updated very easily with noloss in forecast accuracy, and evenimproved estimates of future demand.

This paper shows that overall regulardomestic passenger transport demandcan be forecasted as an aggregate vari-able using time series, thus avoiding a

set of unreliable hypotheses such asthe rates adopted for forecasting futureGDP which are rarely borne out. Infact, if actual GDP growth rates areused and this is the variable that pre-dominates in the econometric model to evaluate the accuracy of the estimat-ed models, actual demand is observedto distance itself even further than theforecast offered in this study. This indi-cates that the forecast is based on a verypoor estimate of the explanatory vari-able, which does not recommend theeconometric model as appropriate forforecasting, even though it does pro-duce good statistical results for theparameters estimated in the model. Thispaper discusses the forecasts of themost recent version of the overalldemand study prepared by Brazils civilaviation department (DAC, 2000) andcompares it with the results from a sim-ple time series model.

Although there is a great deal of uncer-tainty as regards the accuracy of fore-casting models, managerial and par-ticularly investment decisions largelyinvolve forecasts of some kind.Makridakis and Wheelwright (1989)offer a ample discussion of managerialforecasting methods. They emphasisethat the choice of which model to usedepends largely on the analysts knowl-edge. In that regard, they suggestanalysing the various possible modelsby using out-of-sample information asthe criterion for ascertaining which isthe most appropriate. Pindyck andRubinfeld (1991) consider that con-structing predictive models is an art dif-ficult to describe in words, because it

RESEARCH

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Air Transportation Analysis:Passenger Demand in BrazilThis article examines the evolution of overall domestic air passenger transport demand in Brazil,considering recent changes that have affected civil aviation markets, particularly the Brazilianmarket. Although only the Brazilian domestic market is discussed, it has been affected by world-level economic changes. The Department of Civil Aviation, responsible for air transport sectorplanning in Brazil, traditionally uses econometric models to forecast how passenger demand willevolve. However, such modelling introduces great uncertainty into the process of forecasting inde-pendent variables. A time series methodology is used to question the results obtained in traditio-nal modelling. Using a time series approach, the forecasts for overall domestic passenger demandcan be seen to offer better consistency. Econometric models offer a good level of explanation ofthe phenomenon, but rather uncertain results when used for forecasting.

By Elton Fernandes and Ricardo Rodrigues Pacheco

consists largely in intuitive judgementsthat take place in the modellingprocess. Zografos and Madas (2003)discuss approaches to managing airportservice demand and supply. Their dis-cussion centres on the increasingly lim-ited slack between airport service sup-ply and demand, which poses the issueof managing demand against availablecapacity. They observe that, as air traf-fic has grown continuously, demandmanagement has become highly promi-nent among the concerns of air sectormanagement and policy-makingauthorities. What can be seen in the lit-erature generally is that research hasconcentrated on demand managementissues (Brueckner, 2002 and 2005;Daniel, 1995; Daniel and Pahwa, 2000;Le et al., 2004; Schank, 2005). Grubband Mason (2001) discuss aggregatepassenger demand forecasting in theUnited Kingdom. Using the Holt-Winters method they show that demand

trend is the main component in long-term airline passenger forecasting.They conclude that, for estimatinglong-termdemand, forecasting by wayof single univariate time series hassome advantages over forecasting bymultivariate econometric models.Univariate forecasting depends only onthe time series observed in the past andnot on estimating relationships betweenthe series and exogenous variables, andneither does it depend on forecastingexogenous variables, which itself canbe subject to great uncertainties. Byanalyzing the most recent passengerk-ilometre figures published officially bythe air transport authority in Brazil, thisstudy confirms the arguments of Grubband Mason (2001) for using time seriesin forecasting air transport demand.

MethodologyIn generating the forecasts of the uni-variate series, the Holt (1957) expo-nential smoothing model was used. Inorder to produce the forecasts, thismodel uses smoothed estimates for thetrend and for the series level, and usestwo smoothing constants with valuesbetween 0 and 1. Equation 1 shows theforecasting model.

Case studyUntil 2006 the authority governingBrazils Sistema de Aviao Civil

(SAC) was the Departamento deAviao Civil (DAC), attached to theMinistry of Defence. In 2006 therecently created Agncia Nacional deAviao Civil (ANAC) is absorbing

that departments functions. The DAC,meanwhile, is conducting studiesthrough its Instituto de Aviao Civil(IAC) to generate input to civil avia-tion policy making in Brazil. Amongthe periodical studies it makes is theoverall demand study (DAC, 2000),which includes forecasts of passenger,cargo and mail traffic demand to 3, 5and 10 year horizons. As 1997 was themost recent data-year available to thestudy considered here, the forecasthorizons are 2000, 2002 and 2007. Inthe case study in question the authorsconcentrate on discussing passengerkilometre demand in regular domestictraffic in Brazil and analyse forecastsfor 2000 and 2002. The DAC studyinvolves a multivariate econometricmodel with one independent and threeexplanatory variables. The independ-ent variable is the domestic passengerkilometre (PKTD), the explanatoryvariables are Brazils gross domesticproduct (GDP), mean revenue yieldper domestic passenger kilometre(YPD), and one dummy variable withthe value 1 (one) for the period from1992 to 1997 and also throughout theforecast period. This variable absorbs

the fall in demand levels that occurredbetween 1991 and 1992. The estimatedmodel, the Napierian logarithm (LN)of the variables in brackets, is shown inequation 4.

Statistical tests of this model (t statisticof the parameters, R2 regression adjust-ment, regression F statistic and DWautocorrelation of residuals) give goodresults, confirming the validity of theestimated parameters. The hypothesisused in defining projected GDP wastaken from a study by Brazils econom-ic and social development bank (Almet al., 1997). The study was carried outby the planning sector of the bankseconomic development department. Inorder to project YPD, a log-linearregression was adjusted (equation 5)considering ANO (year) and a dummyvariable with value 1 (one) in years1995, 1996 and 1997, as well as in theforecast years.

In this model, the results of the statisti-cal tests (t statistic of the parameters,R2 regression adjustment, regression Fstatistic and DW autocorrelation ofresiduals) are not as good as those forthe demand forecast model.Nonetheless, they can be said to con-firm the validity of the estimatedparameters. In this context, for its fore-casting between 1997 and 2002, theDAC used the following GDP annual

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growth forecast hypotheses: 3% pes-simistic; 4% mean; and 5% optimistic.Using equation 5, the following YPDvalues, in R$ per passenger kilometre,were forecast with a 95% confidenceinterval: pessimistic 0.188376 (2000)and 0.180629 (2002); mean0.147884(2000) and 0.139424 (2002); opti-mistic 0.107392 (2000) and0.098218 (2002). Using equation 4,the following PKTD, in millions,were forecast with a 95% confidenceinterval: pessimistic 15124 (2000)and 16651 (2002); mean 16739(2000) and 19033 (2002); optimistic18876 (2000) and 22234 (2002).

The PKTD values (in millions) actu-ally observed in years 2000 and 2002were 21219 and 28122, respectively.Considering the PKTD values actuallyobserved in years 2000 and 2002, therewas a reasonable difference betweenthe forecast and estimated values. Theactual values are even greater than theoptimistic estimate. This demonstratesthat equation 4 did not produce appro-priate forecasts, despite the impressionof trustworthiness given by statisticaltesting.

Another important point is how theindependent variables of the modelevolved. Firstly GDP: the meanhypothesis of 4% annual growth wouldindicate GDP growth of 12.49% from1997 to 2000, and 21.67% from 1997 to2002. Actual GDP growth was 5.32%from 1997 to 2000, and 8.76% from1997 to 2002 (IPEA, 2006). Thus,applying actual observed GDP to equa-tion 4, the values would be even lower,indicating that the relations estimated inequation 4 were not corroborated forthe future. A second point is the YPDvariable: this is projected by way of anannual trend, which was subjected toregression adjustment using a dummyvariable. The YPD values actuallyobserved for years 2000 and 2002, inR$ per kilometre, were 0.2539 and0.2916, respectively (DAC, 2006).These values are much higher than theforecast values, and as their coefficientis negative in equation 4 this wouldentail still further reduction of the fore-cast values.

Time series results and discus-sionApplying the time series methodologydescribed in item 2 of this paper, usingthe same data series from 1966 to 1997,values of 0.99 and 0.33 were produced,respectively, for the smoothed parame-ters ? and ? , resulting in estimates

much closer to the values actuallyobserved in 2000 and 2002. Table 1shows the forecasts obtained in the95% confidence interval; 2.5% for thelower limit and 97.5% for the upperlimit.

Note that, with 95% confidence, thevalues actually observed lie betweenthe mean and upper limits for the fore-casts produced by the time series model(equation 1). Meanwhile, using themultivariate econometric model (equa-tion 4) at the same level of confidence,the values are well above the upperlimit. In addition, the independent vari-ables of the econometric model werevery distant from the values actuallyobserved, aggravated by the fact thatthey were slanted in order to produce ahigher estimate for example, muchhigher GDP growth than observed and,conversely, a much lower Yield fore-cast than observed.

Although working with a short timeseries, this model is more accurate thanthe multivariate econometric model. Itis certainly much easier to monitor andupdate the process of forecastingthrough time series models, which doesnot entail making hypotheses aboutexogenous variables. The hypothesespresented for forecasting using theeconometric model proved very distantfrom the future reality. Statistical test-ing of the econometric model gave afalse impression of accuracy. The rela-tionship between the structure of the airtransport sector and socio-economicvariables seems to be changing inBrazil. The facts observed here indicatethat income elasticity (GDP proxy) isrising, thus not confirmingpast relationships.

ConclusionThe comparative analysis presented inthis paper shows the benefits of usingtime series in the process of forecastingair transport demand: they are accurateand simple to apply. The intention is notto criticize studies that use econometricmodels to explain the phenomenon,because such models are very useful for

understanding the socio-economic rela-tionships governing the sector and, inaddition, they are a significant aid in theplanning process. The good resultsobtained here recommend a continuousprocess of time series use, adding fur-

ther information in each period.Such a procedure should lead to abetter understanding of sectortrends, as shown in the study byGrubb and Mason (2001).Extending the series should lead tomore accurate forecasting with nar-rower confidence intervals.

ReferencesAlm, A.C.D., Giambiagi, F. and Pasoriza, F.(1997) Cenrio Macroeconmico 1997-2002, BNDES - Banco Nacional de

Desenvolvimento Econmico e Social, Braslia.Brueckner, J.K. (2002), Internalization of airportcongestion, Journal of Air TransportManagement, 8, 141-147.Brueckner, J.K. (2005), Internalization of airportcongestion: a network analysis,International Journal of Industrial Organization,23, 599-614.DAC (2000), Demanda Global, Departamento deAviao Civil do Ministrio da Defesa do Brasil,Rio de Janeiro (www.dac.gov.br, January 2006).DAC (2006), Anurios de Transporte Areo 1998-2003, Vol. II Dados Econmicos,Departamento de Aviao Civil (www.dac.gov.br,January 2006).Daniel, J.I. (1995), Congestion pricing andcapacity of large hub airports a bottleneckmodel with stochastic queues, Econometrica,63, 327- 370.Daniel, J.I. and Pahwa, M. (2000), Comparisonof three empirical models of airport congestionpricing, Journal of Urban Economics, 47, 1-38.Grubb, H. and Mason, A. (2001), Long lead-time forecasting of UK air passengers by Holt-Winters methods with damped trend,International Journal of Forecasting, 17, 71-82.Holt, C.C. (1957), Forecasting Seasonals andTrends by Exponentially Weighted MovingAverages, Research Memorandum No. 52,Office of Naval Research.IPEA (2006), IPEADATA Dados macro-econmicos e regionais, Instituto de PesquisaEconmica Aplicada, (www.ipea.gov.br, January2006).Le, L., Donohue, G. and Chen, C.H. (2004),Auction-based slot allocation for traffic demandmanagement at Hartsfield Atlanta Internationalairport a case study, Transportation ResearchRecord, 1888, 50-58.Makridakis, S. and Wheelwright, S.C. (1989),Forecasting methods for management, JohnWiley & Sons, New York.Pindyck, R.S. and Rubinfeld, D.L. (1991),Econometric models and economic forecasts,McGraw-Hill International Editions, New York.Schank, J.L. (2005), Solving airside airport con-gestion: why peak runway pricing is not work-ing, Journal of Air Transport Management, 11,417-425.Zografos, K.G. and Madas, M.A. (2003),Critical assessment of airport demandmanagement strategies in Europe and the UnitedStates comparative perspectives,Air Transportation Challenges: Airspace,Airports, and Access. Transportation ResearchRecord, 1850, 41-48

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