Toll Road Forecast Risk Analysis using Time Series Models and Portfolio Optimization
Corresponding Author: Rohan Shah, CDM Smith
Presented By: Rohan Shah, CDM Smith, Inc.
Abstract
Toll road planning often encounters decision-making under à priori uncertainties such as market volatility and unpredictable economic development. With a view to mitigate the effects of uncertainty, the study develops a method to jointly manage forecast expectations and inherent risks. Financial economics tools including modern portfolio theory (MPT) and stochastic time series models are used. A portfolio in this context is the set of forecasting tools, models, or options available to planners for estimating future traffic across the facility. MPT proposes diversification among these options with a view to spread out the risks. Econometric time series models with proven forecasting capabilities are used as hypothetical forecast options for modeling purposes. Two univariate time series models are used— Autoregressive Integrated Moving Average (ARIMA), and Brownian Motion Mean Reversion (BMMR) models. Historical time series of traffic data offered by brownfield corridors are utilized for developing forecast estimates, and Monte-Carlo simulation is used to quantify their à priori risks or variance. Optimal forecast portfolios are developed using mean-variance optimization strategies. Numerical analysis is presented using actual historical toll transactions along the Massachusetts Turnpike system. Suggested diversification strategies are found to achieve better forecast efficiencies in the long-term, with better tradeoffs between expected returns and risks. Some resulting specifications achieve efficient risk-return tradeoffs, but also carry higher forecast variance and increase the net risks of the overall forecast portfolio. For the current dataset, some ARIMA specifications appear aggressive in projections compared to BMMR, which exhibits lower variance. The choice of forecasting models or combinations can vary depending on unique risk-proclivities of agencies and the facility under consideration. Practically speaking, agencies and financers are generally expected to be more risk-averse with regard to forecasts especially in the early stages of planning. Single-point forecast streams from travel demand-model based traffic and toll revenue (T&R) studies can be overlaid with probabilistic streams from stochastic time series models such as in this study, and also used to supplement or cross-check forecasts. This can help develop an early understanding of à priori risks associated with long-term traffic forecasts and toll revenue potential, and also improve forecast reliability.