Short-term Forecast Model of Vehicles Volume Based on ARIMA Seasonal Model and Holt-Winters

In order to alleviate the urban traffic congestion and ensure traffic safety, we need to do a good job in urban road traffic safety planning, make the real-time analysis and forecast of urban traffic flow to detect changes of current traffic flow in time, make scientific planning of roads and improve the road service ability and the transport efficiency of freight vehicles. The data of short-term vehicles volume is characterized by uncertainty and timing correlation series. Given this, the ARIMA seasonal model and the Holt-Winters model are used to establish a forecasting model for the short-term vehicles volume of the city. Finally, we compare the model with predictions.


Introduction
City vehicles volume is one of the important basis for the preparation of urban development planning, and it is also an important basic data for economic evaluation and post evaluation of urban construction projects.For the accurate forecast of vehicles volume, it can help transport the traffic control department of scientific management, to ensure the traffic safety.Short-term forecast of vehicles volume is mainly based on a period or even the daily traffic flow changes at the start, to study the short-term variations in the flow of goods vehicles.The short-term vehicles volume is a non-stationary time series [2] with both seasonal and periodic trends [1] and with some diversification.
Because of these attributes, the two typical time series prediction models of ARIMA and Holt-Winters are used to forecast the vehicles GPS data between October 20, 2015 to November 06, 2015 of Kunming, Yunnan Province to analysis and processing.
Traditional predictive methods must collect significant amounts of data, synthesize the various factors that affect the volume of the vehicle collecting data are difficult [3].This type of forecasting method's hard to model.Sometimes the model can be successfully established, but the model parameters are lacking the necessary data and can't be reasonably estimated [4].Because there are two significant characteristics of urban vehicles volume: Firstly, the data varies with the seasons and has a certain periodicity; Secondly, the series formed by the volume of the urban vehicle can be treated as a random series.We can use the ARIMA and Holt-Winters prediction model to approximate the series.When the random series matches the prediction model, the future value can be predicted by the time series and the current value [5].Therefore, we build the forecasting model of urban vehicles volume to improve the accuracy of forecasting.Aim to plan the road traffic system scientific and improve the transportation efficiency of vehicles.

Data Source
The establishment of this model mainly selects the GPS data of vehicles in Yunnan Province from October 20, 2015 to November 16, 2015.Obtained the hourly vehicles volume data of 19 major cities in Yunnan Province after data preprocessing and preliminary statistical analysis.Choicing the 18 days vehicles volume data of city ID as 01 of Kunming to construct the model.The data example shown in Table 1: the p is the degree of nonseasonal autoregressive [7], d is the number of differentials, q is the moving average order [8]; P is the seasonal automatic regression order[9], D is the seasonal time differences, Q is the seasonal moving average order; S is the seasonal period [10].The complete structure of the ARIMA seasonal model is as follows t Y is the non-stationary time series at time t , t ε is the white noise process, s is the cycle step, the study of the vehicles volume sequence has obvious cyclical and using the hourly data as the unit of seasonal data, so the 24 s = , x is the hysteresis operator.
) (x θ is the moving average coefficient polynomial of degree q , ) (x φ is the autoregressive coefficients polynomial of degree.
is the autoregressive coefficients polynomial of degree P [11].
ARIMA seasonal model establishment steps: • Test series smoothness.By observing the time series scatter plot, check whether the unit root exists and the ACF, PACF graph to determine whether the sequence is smooth.For the non-stationary sequence, it can be smooth by difference operation.
• Model identification and parameter fitting.According to the time series ACF graph and PACF graph to select the appropriate parameters of the seasonal ARIMA model to fit.
• Parameter estimation.Using the AIC criterion to determine the model parameters, compare the AIC values of each parameter model, select the model with the smallest AIC value as the optimal model.
• Model test.The residuals white noise test of the constructed model to determine whether the model is feasible.
• Model prediction.Use the established model to predict future time series.

Holt-Winters Model
Holt-Winters model is based on the statistical time series forecasting model, which can predict the time series with no distinct function rules but does correlate and seasonal trend.The time series of seasonal fluctuation, random variation and linear trend are decomposition, combined with exponential smoothing method to estimate the amount of decomposition and establish the prediction model.
The Holt-Winters seasonal model based on the addition is added to the horizontal component and the seasonal component [12].The complete definition of the model is as follows: The t is the time of the time series.t l is the horizontal component, t b is the trend component, t s is the seasonal component, m is the set seasonal period, h is the prediction period, the constant γ β α , , is the smoothing coefficient.
The Holt-Winters seasonal model based on multiplication is the horizontal component multiplied by the seasonal component.The complete definition of the model is as follows: ˆ( ) The t is the time of the time series.

ARIMA Experimental Results
Perform the white noise test on the original sequence; The results shows the , indicate that the original sequence is a non-white noise sequence [13], which has the significance of the research.The vehicles volume shows the significant seasonal characteristics by per hour in Kunming.Tested by ADF, getting the probability of corresponding statistics is 0.01, Rejecting the assumption that the original sequence is a non-stationary series, the result shows that the vehicles volume time series are stationary, which consistent with the observations observed in Figure 1.  2, the original sequence was diagnosed as a trend stationary, seasonal non-stationary series [14,15].So we make the onedegree difference to the series.So the .The parameter q of the ) (q MA can be determined by the truncation of the AC, the parameter p of the ) ( p AR can be determined by the truncation of the PAC.From the Figure 2 we can do analysis that it could be possible the value of p could be 0 or 1, the value of q could be 0 or 1, the value of P could be 0 or 1, the value of Q could be 0 or 1.

χ
, which demonstrate that the series information of vehicles volume has been fully extracted, and the series model residuals are white noise series.The final model is identified as the optimal model [16].Table 6 shows the experimental comparing result of the ARIMA and Holt-Winters.The ARIMA seasonal model has the higher predictability of vehicles volume data, and the predicted mean square error and mean error also lower than the Holt-Winters model.

Conclusion
The ARIMA seasonal model and the Holt-Winters model are used to forecast vehicles volume of Kunming in Yunnan Province.The forecast value was compared with the actual value, we can conclude that the ARIMA seasonal model is used to predict the volume of the vehicle are better than Holt-Winters model, and the ARIMA seasonal model has a higher fitting degree and better forecasting error.Due to limited data, and there are many factors that affect the volume of the short-term vehicle, the forecast model has some errors.Other factors should be considered in the actual application.

Figure 1 .
Figure 1.Original data time series graph graph and partial autocorrelation graph, we can obtain the p and q value in the

2 R
is 0.987, indicated that the model is highly fitted.The data fit graph is shown in the blue section of Figure3.The model residual graph is shown in Figure4.

Table 1 .
[6]icles Volume Data Example time series with seasonal and trendy urban vehicles volume, the stationary time series can be obtained by periodic series difference and seasonal series difference.ARIMA seasonal model can extract the time series characteristics of seasonal, trend and random errors in the vehicles volume series.Through the timing diagram and the result of difference operation[6], the vehicles volume predict model was determined as the

Table 3 .
Combination Of Arima Seasonal Model

Table 4 .
Arima Seasonal Model Fitting Degree Statistics

Table 5 .
Holt-Winters Model Fitting Degree Statistics

Table 6 .
Model Fitting Degree Statistics