Three Novel Methods to Predict Traffic Time Series in Reconstructed State Spaces

Introduction

Traffic time series is referred to as temporal evolution of traffic parameters (e.g., flow, speed, and occupancy) measured in a chronological order with identical time interval. Accurately capturing and predicting the temporal evolution of traffic parameters is prerequisite for developing and implementing many intelligent transportation systems (Stephanedes et al., 1981; Chang & Miaou, 1999; Lam et al., 2005). A smart adaptive signal control, for instance, is oftentimes established on the basis of instantaneous or predicted short-term (e.g., 5-minute) traffic data. Advanced incident detection may require even shorter-term (e.g., 1-minute) traffic data as inputs (Lan & Huang, 2006).

Techniques for predicting traffic time series can be categorized in different ways, including parametric (e.g., historical mean value algorithm, regression method, neural network algorithm, time series method, Kalman filtering, compound forecasting algorithm) versus nonparametric (e.g., nonparametric regression method, wavelet filtering method), linear (e.g., autoregressive moving average or ARMA model, autoregressive integrated moving average or ARIMA models) versus nonlinear (e.g., nonlinear ARIMA, fuzzy local reconstruction method, fuzzy neighborhood method, state-space local approximation method), among others. To save space, the present article has no intension to exhaust all the relevant works on traffic prediction. A state-of-the-art review on the traffic predicting techniques has been done by Van Arem et al. (1997) and Vlahogianni et al. (2004). However, the literature on traffic prediction is full of differing conclusions and it is never easy to make a general statement.

For example, Smith and Demetsky (1997) compared historical average, time-series, neural network, and nonparametric regression models and concluded that the nonparametric regression model significantly outperformed the other models and was also easier to implement. Durbin (2000) claimed that the state space approach has advantages over the ARMA models or ARIMA models. Smith et al. (2002) compared parametric and nonparametric models and concluded that using nonparametric regression coupled with heuristic forecast generation methods would perform better than a naïve forecasting approach, which also outperformed over a classic parametric modeling approach (e.g., seasonal ARIMA models). Taking the superior capability of neural networks to approximate a nonlinear system, however, the nonlinear ARMA (NARMA) model has been claimed satisfactorily in nonlinear prediction (Bonnet, 1997).

A considerable number of literature adopted time series analysis for traffic prediction purposes (e.g., Head, 1995; Lee & Fambro, 1999; Lingras et al., 2000; Lam et al., 2006). Many literature showed that neural networks are one of the best alternatives for modeling and predicting traffic parameters because they can approximate almost any function, regardless of its degree of nonlinearity and without prior knowledge of its functional form (e.g., Clark, et al., 1993; Kirby et al., 1997; Ishak et al., 2003; Vlahogianni et al., 2005; Sheu et al., 2009). Other literature also elaborated the traffic predicting techniques with Kalman filtering (e.g., Okutani & Stephanedes, 1984; Sun et al., 2003; Wang & Papageorgiou, 2005), wavelet analysis (He & Ma, 2002; Li, 2002; Soltani, 2002), and multivariate state space approach (Stathopoulos and Karlaftis, 2003; Lan et al., 2007).