This chapter focuses on the presentation and analysis of the autoregressive integrated moving average (ARIMA) family of models for forecasting time-series that are mathematical models of the persistence, or autocorrelation (correlation across values), in a time series. Unlike the use of time series in regression, ARIMA models describe the behavior of a variable in terms of its past values. These models are rather simple and straightforward to develop and are useful for forecasting time series even in the absence of explanatory variables. ARIMA models are widely used in almost all fields of transportation with marked success, and this is discussed in the chapter. The chapter also presents discussions on nonlinear models including bilinear models, threshold autoregressive models, functional parameter autoregressive models, and neural networks.