A Time Series Analysis of Rail Demand in Great Britain

A Time Series Analysis of Rail Demand in Great Britain


G Whelan, MVA Consultancy, UK; A Harvey, University of Cambridge, UK: J Cartmell, Department for Transport, UK


The paper investigates the time-series characteristics of the demand for rail travel in Great Britain over the past 30 years.


The paper explores the characteristics of time-series data to help understand how best to model the demand for rail travel. More specifically, the paper:

- Explores the relationship between rail demand and economic performance, considering the influence short and long term trends, and the existence of asymmetric effects (e.g. gains and losses);

- Examines the impact of long-term trends in economic, demographic and competition variables;

- Examines the impact of long-term trends in endogenous factors such as fares and service quality;

- Identifies and assess the influence of structural breaks on demand whether as a result of a single event or a process evolving over time; and

- Considers the constraints to passenger demand growth brought about by demand (market saturation) and supply (capacity restriction) side factors.

The methodological approach includes the use of univariate time-series and multivariate econometric approaches as well as a new application of unobserved component models (Harvey, 2006). Each model specification has advantages and disadvantages but on balance the unobserved components model is our preferred approach as it allows for trend and seasonal components to evolve over time allowing for changes to omitted variables and changes to consumer tastes and preferences. The unobserved components approach is thought to generate more robust elasticity estimates but it also identifies an unexplained trend which will need to be accommodated in the production of forecasts.

In addition to fares and economic performance, the models also included a range of other significant influences including: rail performance as measured by the Public Performance Measure (PPM), an index of the cost of motoring/price of fuel, an index of Bus & Coach fares and a series of dummy variables to account for accidents, strikes and regulatory interventions.

The analysis suggests that:

- A constant elasticity functional form is appropriate;

- There are no substantial structure breaks/ time varying parameters;

- There is limited evidence of behavioural asymmetries when modelling economic gains and losses;

- The use of a simple average revenue as a proxy for fares is problematic as shifts in demand between different products at different times of the year can result in volatility in the average revenue estimate. This volatility can be reduced by estimating the underlying trend in average revenue;

- Dynamics are important but their specification needs careful interpretation; and

- Fare elasticities of demand (passenger kilometres) are around -0.65 for Season tickets and around -0.9 for Non-Season tickets.


Harvey, A.C. (2006) Forecasting with Unobserved Components Time Series Models, Handbook of Economic Forecasting, edited by G Elliot, C Granger and A Timmermann, 327-412. North Holland.


Association for European Transport