The key to effective decisionmaking, in transportation as elsewhere, is to understand the workings of the system in order to make accurate assessments of future developments. In this special issue of JTS on transportation forecasting, we have tried to select papers that both examine transportation issues of interest and provide examples of state-of-the-art approaches to forecasting.
The six papers in this special issue are grouped into three areas: economic modeling, surface transportation, and air transportation. The forecasting methods range from single equation time series procedures to detailed econometric models, and the forecast horizons include the short term (typically a few months) through to the long term (five years or more).
Time series methods typically emphasize effective forecasting, whereas econometric models allow the decisionmaker to gain a deeper understanding of the structure of a system. Thus, the two approaches are complementary and, of course, partially overlapping. In the first paper, Fullerton develops an econometric forecasting system to study two cross-border metropolitan areas: El Paso, Texas, and Ciudad Juárez, Mexico. Within this system, the author models two blocks of transportation equations: northbound surface traffic across the bridge at Ciudad Juárez; and passenger, cargo, and mail flows at the El Paso airport. The model is then used to forecast surface and air traffic in the region.
Liu and Vilain use input-output analysis to estimate commodity inflows in the United States. Using data from the 1993 Commodity Flow Survey (CFS), the authors demonstrate a method for estimating freight inflows on a smaller, substate, regional basis and base the estimates on the industrial structure of the region. Because the CFS only disaggregates data to the state level, Liu and Vilain test the accuracy of their method by estimating flows at the state level and then comparing their results to the actual state results.
Surface transportation systems often require rather detailed forecasts of passenger flows over relatively short time horizons. García-Ferrer et al. develop forecast models for monthly bus and Metro ticket demand in Madrid, Spain. Incorporating changing seasonality, calendar effects, and several interventions, the authors compare forecast results from a dynamic transfer-function model and a variant of an unobserved component model.
In an article that studies safety concerns, Raeside studies trends in highway casualties in Great Britain for both travelers and pedestrians. From these time series models, he provides forecasts through 2010 of the casualty rate per kilometer and then compares these forecasts to government-set targets to assess if they are achievable.
Estimating the impact of September 11, 2001, on U.S. air travel, Ord and Young provide a method for quickly estimating three aspects of the intervention for monthly time series measures of air travel. By creating three separate components of the eventan additive outlier, a level shift, and a temporary decaythe authors illustrate how the combination of the three interventions can be used to adjust a time series only a few months after a major event occurs.
The paper by Bhadra and Texter examines changes in the structure of airline networks in the United States. The growth of low-cost airlines and the increased use of regional jets have provided the impetus for the industry to reconsider the value of the traditional hub-and-spoke system and the authors examine the impact of these changes on airline networks.
If the reader is a novice to the forecasting literature, he or she may be confronted with vocabulary or ideas that are new. We hope the following brief synopsis of some of the terms used in this issue will be helpful.^{1}
In addition to measures of seasonality of the data, some models incorporate additional interventions that reflect consequences of the calendar. Terms such as trading days and holiday effects indicate interventions that reflect the differing number of business days in a particular month (trading days) and the differing position of some holidays in the month (e.g., Easter and Thanksgiving do not fall on the same date every year). Some seasonality procedures may not be able to handle the changes in these effects, so dummy variables may be introduced to reflect their impact.
In order to measure a model's ability to forecast unknown future values, a set of data points from the end of the series is sometimes withheld during model estimation. The withheld data points, called hold-out observations, can then be compared with forecasted values of this period to evaluate the accuracy of the forecast.
In ex-ante forecasting, a hold-out sample of both the explanatory and dependent variables is created and removed. Forecasts are generated for the explanatory variables and then used to forecast the dependent variables. The result is a true forecast. Ex-post forecasts typically use the actual values of the explanatory variables. In addition, models producing ex-post forecasts may not use any hold-out sample at all, resulting in all the data being included in the model estimation.
Model fit measures like MSE (mean square error) may not be very informative when trying to compare models that have different numbers of parameters. In order to compare models, measures such as Akaike's Information Criterion (AIC) and Bayesian Information Criterion (BIC) may be used. The general structure of such measures is: "goodness of fit measure" + "penalty function" and represents a tradeoff between fit and model complexity. For example, the AIC may be written as
A I C = nlog_{e }M S E + 2k
The coefficient k denotes the number of parameters fitted. These measures allow quality-of-fit comparisons across models with differing numbers of variables.^{2}
In addition to the familiar figures of MSE and R^{2 }(the coefficient of determination or proportion of variance explained), forecast procedures employ statistics that measure different aspects of the quality of the model. Since model fit is not an adequate way to assess forecasting performance, in these articles forecast performance may be assessed either by using information criteria or by using measures based on the hold-out sample. In addition to MSE, authors also use the mean absolute deviation (MAE) and the mean absolute percent error (MAPE).^{3}
If the researcher has developed only one model, he or she could still compare the results against the simplest of the forecast methodstermed the "naïve" modelwhich usually consists of a forecast repeating the most recent value of the variable (e.g., the best forecast of a stock price today is the price of that stock yesterday). The model underlying this naïve forecast is the random walk, which can be specified as
y_{t} = y_{t - 1} + ε_{t}, where ε_{t} ~ i.i.d. N (0, σ ^{2}) .
That is, each value in the time series is the previous value plus some noise. We may then compare a selected model to the random walk. Behind this notion is the belief that if a forecasting model cannot do better than a naïve forecast, then the model is not doing an adequate job. Theil's U is a statistic that uses the random walk as a benchmark for comparing the quality of forecast models.
As expected, we received more articles than could be incorporated into one issue. We want to call your attention to three articles, in particular, that we expect to publish in the near future. We originally thought this issue would contain both general transportation forecasting research as well as special articles describing current forecasting models used by the Department of Transportation (DOT). But space required that we delay publishing the two articles dealing with the DOT models until a later issue. A paper by David Chien of the Bureau of Transportation Statistics will present an evaluation of some of the models for greenhouse gas emissions. Roger Schaufele will summarize the models used by the Federal Aviation Administration to forecast large U.S. air carrier domestic revenue passenger-miles, domestic passenger enplanements, and domestic revenues.
The third article we plan to publish is by Miriam Scaglione (Institute of Economy and Tourism, Switzerland) and Andrew Mungall (Lausanne Institute for Hospitality Research, Switzerland), who study interventions with respect to international air travel. They analyzed the impact on Swiss air traffic of Swissair's decision to concentrate all long-haul flights through Zurich and its subsequent filing for bankruptcy. They also look at how air traffic in Switzerland was affected by the terrorist attacks in the United States.
The special issue has generated considerable interest in transportation and forecasting in such groups as the Transportation Research Board and the International Institute of Forecasters. We expect this interest to result in a number of forecasting papers in future issues of JTS.
Keith Ord |
Peg Young |
We wish to thank all the diligent work by the numerous referees as well as by the JTS editorial staff. While we cannot list the referees by name at this time, we can at least comment that their insight and careful review made each and every article a better piece of research, as also noted by every author. Names of the JTS staff we can mention and publicly thank: Jack Wells, Marsha Fenn, Alpha Glass, Jennifer Brady, Dorinda Edmondson, Martha Courtney, and Lorisa Smith. With all their work and advice, we feel confident that transportation forecasting will be appreciated by a wider audience.
Armstrong, J.S., ed. 2001. Principles of Forecasting: A Handbook for Researchers and Practitioners. Boston, MA: Kluwer Academic Press.
Harvey, A. 1997. Trends, Cycles and Autoregressions. The Economic Journal 107:192201, January.
Kennedy, P. 1998. A Guide to Econometrics, 4th ed. Cambridge, MA: The MIT Press.
Makridakis, S., A. Anderson, R. Carbone, R. Fildes, M. Hibon, R. Lewandowski, J. Newton, E. Parzen, and R. Winkler. 1982. The Accuracy of Extrapolation (Time Series) Methods: Results of a Forecasting Competition. Journal of Forecasting 1:111153.
Makridakis, S., C. Chatfield, M. Hibon, M. Lawrence, T. Mills, J.K. Ord, and L. Simmons. 1993. The M-2 Competition: A Real-Life Judgmentally Based Forecasting Study with Discussion. International Journal of Forecasting 9:522.
Makridakis, S. and M. Hibon. 2000. The M3-Competition: Results, Conclusions and Implications. International Journal of Forecasting 16(4):451476.
Makridakis, S., S.C. Wheelwright, and R.J. Hyndman. 1998. Forecasting Methods and Applications, 3rd ed. New York, NY: John Wiley & Sons., Inc.
^{1.} An excellent glossary of forecast terms can be found in Makridakis et al. (1998) or on the Principles of Forecasting website maintained by Professor Scott Armstrong of the University of Pennsylvania, available at http://morris.wharton.upenn.edu/forecast/dictionary, as of November 2004.
^{2.} For an interesting series of forecast competitions, we suggest the reader pursue the literature on the M-competition (e.g., Makridakis et al. 1982, 1993; and Makridakis and Hibon 2000).
^{3.} Armstrong (2001), Harvey (1997), and Kennedy (1998) are just a small subset of articles dealing with the model fit versus forecast accuracy debate.