Chapter 6 - Trend Projection and Time Series Methods

Abstract

This chapter deals with trend projection and time series methods for the forecast of transport demand. Assumptions, conditions of use, and suitability of time series methods are first emphasized. The various components of a time series (trend, seasonal, cyclical, random) are identified, and an extensive example of a seasonally adjusted trend projection of air traffic demand (domestic+international) at airports of the United States is analytically explained. Linear and nonlinear (exponential, parabolic second degree, sigmoid curve) forms of trend projection are surveyed. Methodology, successive steps, and the appropriate statistical methods for trend projection forecasts are presented together with a detailed representative example of forecast of passenger demand of Eurostar trains. It is explained how it would be made possible to deduce the most suitable regression curve and equation with the use of regression analysis and calculation of values for the coefficient of determination, how outliers can be checked, and which indexes permit an ex post assessment of a trend projection forecast. Another example of trend projection with ex post assessment of the forecast is explained for the case of tourist demand of an international airport. Other statistical methods of extension of data of the past into the future are given: simple moving average, weighted moving average, exponential smoothing, and trend-adjusted exponential smoothing. All these methods are also applied for the forecast of passenger demand of Eurostar trains. The various time series processes are analyzed: white noise, random walk, autoregressive (AR), moving average (MA), autoregressive moving average (ARMA), integrated ARMA (ARIMA), and seasonal ARIMA (SARIMA). Methods to check stationarity of time series are presented: correlograms (autocorrelation and partial autocorrelation functions) and unit root tests (Dickey–Fuller, Augmented Dickey–Fuller, and others). The various criteria for the selection of the appropriate time series model are explained: Akaike, Bayesian, and Hannan–Quinn information criteria. The Box–Jenkins method, the most popular among time series, is analyzed. All the above are applied in an extensive example of the Box–Jenkins method for the forecast of vehicle traffic in a road section.