###### Abstract
However, in the proposed STARIMA model [11], the weight matrices are assigned equally without considering the traffic condition differences between the directly connected first order spatial neighbors and the not directly connected higher order neighbors in the whole road network. In the past 10 years, there have been many research studies on STARIMA. [PERSON] et al. [12] presented a dynamic form of the STARIMA that accounted for temporal dynamics. They replaced the traditional distance-weighted spatial weight matrix with a temporally dynamic matrix that reflected the current traffic turn ratios observed at each road intersection. The weight matrix can be updated in real time based on current conditions, but the method was limited to intersection-based flow data and was fixed spatially. [PERSON] et al. [13] extended the standard STARIMA model to a Localized STARIMA (LSTARIMA) model, which described the modeling of dynamic and heterogeneous autocorrelation in network data with improved traditional models. The constructed model provided an improvement over the traditional space-time series models. Their paper showed that the performance of prediction was improved when compared to standard STARIMA models. The LSTARIMA model captured the autocorrelation of traffic data locally and dynamically in the road network with a dynamic spatial weight matrix. The LSTARIMA model has also shown good performance in traffic prediction without the need for data pre-processing (e.g., a logarithmic transformation and differencing). Compared with other ARIMA variations, the LSTARIMA model has a simpler structure (because the LSTARIMA has smaller AR, and MA order values \(p\) and \(q\)). As the future traffic state of the current road depends not only on its prior states, but also on its neighbor roads, the weight matrix of roads is key to traffic flow prediction. In this paper, our contributions are as follows:  
1. An LSTAR model with lower computational complexity based on the LSTARIMA was proposed. In the LSTARIMA model of [PERSON] et al. [13], the same weight matrix \(W\) was used for AR and MA components of the whole road network. We used different matrices, \(W\) and \(U\), for AR and MA components. And individual observation \(z_{i}(t)\) was used instead of the \(N\)-dimension column vector \(Z(t)\) to allow each road to have its own weight matrix \(W\), \(U\). Since the ARMA model can be properly approximated by a high-order AR model, we further developed the reconstructed LSTARIMA model into our proposed LSTAR model. 2. A more reasonable weight matrix and new traffic information collection with the Vehicular Ad hoc Networks (VANET) approach was proposed. As the number of vehicles output from upstream roads has more impact on the future traffic condition compared to speed difference, it was used to determine the dynamic spatial weights instead of the speed difference. To obtain the traffic information needed for weight matrix determination, the vehicles stopped at red lights were used to collect traffic information via VANET. 3. Two theorems were given and verified for parameter estimation of our proposed LSTAR model. When the distribution of traffic flow is stable, the weight matrix can be treated as time invariant. When the traffic flow distribution is not stable, the weight matrix is time variant. For these two different cases, we provided two theorems to determine the parameters. 4. Related simulations were performed. Through the simulation results, we observed that the prediction accuracy of LSTAR was a bit lower than the LSTARIMA model. However, the computational complexity of the LSTAR model was also lower than the LSTARIMA model. Therefore, there existed a tradeoff between the prediction accuracy and the computational complexity for the two models. The rest of this paper is organized as follows. In Section 2, state-of-the-art traffic information collection, traffic prediction, and traffic applications are reviewed.