A Multivariate ARIMA Model to Forecast Air Transport Demand
Alberto Andreoni, Maria Nadia Postorino, Mediterranean University of Reggio Calabria, IT
In this work, both univariate and multivariate air transport demand ARIMA models are proposed to estimate the demand levels about Reggio Calabria regional airport (South of Italy) and to analyse the impact of recent modifications in the supply.
The forecast of the air transport demand has a great influence on the development of airport master plans, with respect both to the airside (runways, taxiways, aprons, technological devices) and the landside (boarding/landing area, waiting rooms, etc.). Indeed, they depend on the amount of passengers, that varies during the reference time period (day, week, month, year).
Usually, the estimation of the air transport demand can be obtained by different models/methods, among which time series models and market surveys (RP ? SP methods) are the most used by airline companies.
Time series models use past values of the dependent/independent variables to forecast the future values of the considered variable; they can be grouped in univariate and multivariate models depending on using only past values of the examined variable or also the past values of other explanatory variables.
In this work, both univariate and multivariate air transport demand ARIMA models are proposed to estimate the demand levels about Reggio Calabria regional airport (located in the South of Italy) to capture both the trend of demand and the effects induced by the difference polices adopted at the Reggio Calabria airport. The study was partially funded by the Ministry of High Education and Research, as part of a more general research programme concerning the planning of the development of the regional Italian airports.
The study is particularly interesting because due to the fare policy adopted by the main airline company operating at the airport and the variations in the number and schedule of the flights the passenger demand at the airport changed in the last ten years against expectations (a promising positive trend has been followed by a very strong demand reduction). Recent modifications started by the local airport authority in the supply (new links, new destinations and lower fares) are expected to produce an increase in the air transport demand, also due to induced trips generated by the new supply.
Generally, univariate ARIMA models or simpler autoregressive time series models are the most used by the airline companies, given that the only data to be acquired refer to the planed/enplaned passengers and the results obtained are quite satisfactory.
However the multivariate models allow the demand to be estimated depending on the values of the explanatory variables, and then to simulate the air transport system in order to analyse the effects of the decisions assumed within the different planning policies. This fact can be proved by comparing the univariate and multivariate calibrated models for the specific test case, given that recently some low-cost airlines started flying from Reggio Calabria airport to Venice, Bologna and Turin, thus introducing a significant variation in the supply.
The ARIMA univariate model uses as variable the demand level for the reference time period. To estimate the univariate model, the Box and Jenkins method, which estimates the stochastic process starting from its finite realization by means of a trial and error procedure, is one of the most popular. The crucial point is the analysis of the total and partial autocorrelation functions that allows the identification of non stationary processes both in mean (trend) and in variance; to remove the trend and then to transform the original processes in stationary processes, the series should be differenced while to remove the non-stationariness in variance the logarithmic transformation of data should be used.
Limits of univariate models are the hypothesis of stability of boundary conditions and the inability to simulate how the demand changes according to the variations of some relevant explanatory (or independent) variables.
To overcome these limits, multivariate ARIMAX models can be used. In this case, one or more independent variables can be used to explain the variations of the demand levels in time. From a practical point of view, the introduction of explanatory variables requires the knowledge of their values for the given time periods (as for the demand level). Furthermore, the dependent variable (demand level) depends on the lagged values of the independent variables and then the length of the lag should be estimated by means of a sequential procedure based on statistical tests.
The calibration of both univariate ARIMA models and multivariate ARIMAX models has been obtained by using data of the planned and enplaned passengers at the airport of Reggio Calabria from 1989 to 2004.
The univariate identified model is ARIMA(1,1,2), confirmed by the diagnostic checking on the residuals. The multivariate ARIMAX model considers two explanatory variables: the yearly movements of aircrafts at the airports and the yearly per capita income. The fare variable was also considered one of the most important independent variable to introduce in the model, but data are not available and then some alternative procedures have been developed in order to obtain a shadow estimate of those values (e.g., by using the hedonic pricing theory).
The results obtained with both univariate and multivariate models are all satisfactory in terms of statistical tests, but multivariate models allow some alternative supply policies to be tested thus giving indications about the most useful actions that should be undertaken to guarantee a convenient development of the airport.
Association for European Transport