主要模型及应用 1. ARIMA 2. LSTM  GRU 

1 ARIMA模型

As early as 1976, Box and Jenkins[1] proposed the Autoregressive Integrate Moving Average Model (ARIMA).  In 1995, Hamed et al[2] used the ARIMA model to predict the traffic volume in urban arterials.  To improve the prediction precision of the model, different variants were produced, including Kohonen ARIMA[3], subset ARIMA [4], seasonal ARIMA [5], and so on.These models are based on the assumption of stationary variance and mean of the time series.

[1] M. S. Ahmed and A. R. Cook, “Analysis of freeway traffic time-series data by using Box-Jenkins techniques,” Transp. Res. Rec., no. 722, pp. 1–9, 1979.

[2] M. M. Hamed, H. R. Al-Masaeid, and Z. M. B. Said, “Short-term prediction of traffic volume in Urban arterials,” J. Transp. Eng., vol. 121, no. 3, pp. 249–254, 1995.

[3] M. van der Voort, M. Dougherty, and S. Watson, “Combining kohonen maps with ARIMA time series models to forecast traffic flow,” Transp. Res. C, Emerg. Technol., vol. 4, no. 5, pp. 307–318, 1996.

[4]  S. Lee and D. Fambro, “Application of subset autoregressive integrated moving average model for short-term freeway traffic volume forecasting,” Transp. Res. Rec., J. Transp. Res. Board, vol. 1678, no. 1, pp. 179–188, 1999.

[5]  B. M. Williams and L. A. Hoel, “Modeling and forecasting vehicular traffic flow as a seasonal ARIMA process: Theoretical basis and empirical results,” J. Transp. Eng., vol. 129, no. 6, pp. 664–672, Nov. 2003.

1.1 概念

       求和自回归移动平均模型，(Autoregressive Integrated Moving Average Model,ARIM