40 Transportation Research Record: Journal of the Transportation Research Board, No. 2392, Transportation Research Board of the National Academies, Washington, D.C., 2013, pp. 40–47. DOI: 10.3141/2392-05 Department of Civil, Structural, and Environmental Engineering, University at Buffalo, State University of New York, 231 Ketter Hall, Buffalo, NY 14260. Corresponding author: A. W. Sadek, asadek@buffalo.edu. variables to predict daily traffic volumes (3). A major limitation of SARIMA time series analysis in general, however, is that the mod- els assume linear correlation structures among time series data and, thus, the models may not be able to capture the nonlinearity inherent in real-time traffic data. Nonparametric methods, by contrast, attempt to identify historical data that are similar to the prediction instant and use the average of the identified data items to forecast the future. Nonparametric meth- ods do not rely on predetermined relationship functions between the past and the present and are thus supposedly able to deal with the nonlinearity and nonstationarity of traffic time series. The typi- cal nonparametric methods include computational intelligence (CI) techniques; for example, many different types of neural networks have been proposed (4–5). Besides neural networks, support vec- tor regression (SVR) has also been used (6, 7 ). In addition to CI, another popular class of nonparameter models is nearest neighbor methods (8). Although there is an extensive literature on short-term traffic vol- ume prediction, most of the previous studies considered only one modeling technique and a single data set. Even among the compara- tive studies in the literature, the focus has typically been on compar- ing the performance of multiple models on a single data set (9, 10). The risk of using one data set to test models is that the conclusions derived may be specific to the data set considered. This has often led to inconsistent conclusions among the different studies regarding which modeling method is superior. In addition, single-data–based testing cannot address the essential question that is of particular interest to practitioners (i.e., how to select prediction models based on the data). Recently, a handful of researchers have begun to pay more atten- tion to that issue. For example, Smith and Demetsky tested four prediction methods on two data sets (8). However, the two data sets came from sites on the same highway and there was no discussion in the study about the relationship between the attributes of a data set and model performance. Other researchers have pointed out the impor- tance of data diagnosis before model selection and proposed different measures to indicate data characteristics. For instance, Vlahogianni et al. (11) discussed some statistical methods for detecting nonlinear- ity and nonstationarity of traffic volume time series and Shang et al. (12) discussed the nonlinearity property of traffic volumes based on chaos theory. However, no effort was made in those studies to link data diagnosis results with model selection. In this context, the study reported here used multiple data sets to conduct comprehensive testing of the performance of online traf- fic prediction models. Three popular prediction models, SARIMA, SVR, and k nearest neighbor (k-NN), were chosen as representa- tives of parametric and nonparametric classes. In addition, four data Short-Term Forecasting of Traffic Volume Evaluating Models Based on Multiple Data Sets and Data Diagnosis Measures Lei Lin, Qian Wang, and Adel W. Sadek Although several methods for short-term forecasting of traffic volume have recently been developed, the literature lacks studies that focus on how to choose the appropriate prediction method on the basis of the statistical characteristics of the data set. This study first diagnosed the predictability of four traffic volume data sets on the basis of various statistical measures, including (a) complexity analysis methods, such as the delay time and embedding dimension method and the approxi- mate entropy method; (b) nonlinearity analysis methods, such as the time reversibility of surrogate data; and (c) long-range dependency analysis techniques, such as the Hurst exponent. After the data sets were diagnosed, three models for short-term prediction of traffic vol- ume were applied: (a) seasonal autoregressive integrated moving aver- age (SARIMA), (b) k nearest neighbor (k-NN), and (c) support vector regression (SVR). The results from the statistical data diagnosis meth- ods were then correlated to the performance results of the three predic- tion methods on the four data sets to determine the means for choosing the appropriate prediction method. The results revealed that SVR was more suitable for nonlinear data sets, while SARIMA and k-NN were more appropriate for linear data sets. The data diagnosis results were also used to devise a selection process for the parameters of the prediction models, such as the length of the training data set for SARIMA and SVR, the average number of nearest neighbors for k-NN, and the input vector length for k-NN and SVR. The ability to provide short-term forecasts of traffic flow parameters has long been regarded as a key component of advanced traffic man- agement and control system applications. In the past few decades, a variety of prediction models have been developed for that purpose. Generally speaking, these methods can be categorized into para- metric methods and nonparametric approaches. Among the most popular parametric models are time series analysis methods, such as the seasonal autoregressive integrated moving average model (SARIMA). For example, Williams and Hoel presented the theo- retical basis for modeling univariate traffic condition data streams as SARIMA processes (1). Smith et al. showed that SARIMA per- forms better than the nonparametric nearest-neighbor method for the single-point traffic prediction problem (2). Cools et al. used both ARIMA with explanatory variables and SARIMA with explanatory