Prediction and Analysis of O3 based on the ARIMA Model

Shuangjin LI, Ning YANG, Yiqi YAN, Xudong CAO, Degang JI*

1. Institute of Modern Science and Technology, Hebei Agricultural University, Baoding 071000, China;

2. Faculty of Science Department of Mathematics, Hebei Agricultural University, Baoding 071000, China

Air is life foundation and air quality decides livelihood quality of people. In practice, photochemical smog significantly influences the quality of summer air. It is known that ozone layer in the stratosphere prevents damages from ultraviolet light on life forms.However,ozone near the surface proves a major source of photochemical smog, which would potentially damage crops,trees,and other plants, as well as cause asthma of children[1]. Currently, much more researches have been conducted on prediction on air quality.For example, Si performed prediction on air quality with improved grey neural network combination model(IGNNM),but the effects of pollution source intensity on pollutant concentration are not taken into consideration. Therefore, the prediction is not so precise if air quality changes dramatically. On the other hand,FA-GNNM concerns complicated work and the obtaining of data is much difficult[2].In contrast,Analysis of time series[3]is suitable for middle or short-term prediction with high accuracy.The research made prediction on air quality in following two weeks in Baoding City as per analysis of time series and concluded change rules of pollutants based on prediction results,as well as proposed some suggestions and countermeasures.

Data Source

The research data referred to data monitored by China National Environmental Monitoring Centre[4]and the major pollution index was O3.

Establishment of Model

Data and processing

Some data were missing and replaced by averages of neighboring values.

According to one-sample Kolmogorov-Smirnov test, the detection value of O3was 0.303, which was higher relative to significant level of 0.05. Hence, the sample data were normally distributed and can be used for analysis of time series.

Stabilization of sequence

As shown in Fig.1, the sequence of xt4were unstable, the sequence of yt4was concluded by firstorder difference.

Because sequence yt4tended to be volatile around average, autocorrelation function and partial autocorrelation function were within confidence interval, without regularity. Assuming significance level of α=0.05, it is be-lieved that yt4was relatively stable.Therefore, the model of ARIMA(p,d,q)was establsihed with sequence xt4.

According to changes of autocorrelation function, the data showed periodicity and seasonal differences should be conducted on the sequence.Therefore,ARIMA(p,d,q)(P,D,Q)7 was established with xt4.

As shown in Fig.3,autocorrelation function of xt4was censored with k=1,and partial autocorrelation function censored with k=5. It can be concluded that and non-seasonal model was applied with ARIMA(5,1,1).As shown in Fig.4, both of autocorrelation function and partial autocorrelation function of the first-order difference of xt4were censored with k=2. Therefore, ARIMA(2,1,2) was applied. Meanwhile, data fitting should be considered of ARIMA(1,1,1) (2,1,3) and ARIMA (5,1,1)(2,1,3).

It can be concluded from indices above that it is optimal for fitting and prediction with ARIMA (5,1,1)(2,1,2)models.The research performed fitting on O3in following 14 days with SPSS,as follows:

Table 1 Comparisons of O3 model

Table 2 The predicted values of O3 in following 14 days in Baoding

Model evaluation

An autoregressive integrated moving average (ARIMA) model is a common and effective way in time series analysis and it is fitted to time series data to predict future points in the series,with time (t) as a random variable[5]. The autocorrelation of such random variables indicates extension of predicted objects’ trend and once the autocorrelation is described by mathematical model, future points can be predicted from the past and present values. The research performed analysis on relative errors based on data issued by national environmental monitoring website[4]and concluded the error range was in 5%-15%, so that the prediction model and data were reliable.

Analysis on results

As shown in Fig.5, O3kept increasing in a fluctuated way and it canbe concluded from the predicted values that the concentration of O3was higher. The causes can be concluded as follows:

With economy development, motor vehicles and population keep growing, increasing O3concentrations in Baoding, deteriorated by pollutants from industry, transportation and urban non-point pollution.

O3discharged in urban suburbs is increasing by winds, resulting in high concentration of O3in Baoding.

The lower wind speed on ground in hot summer is conductive to production of photochemical smog and accumulation of pollutants[6].

Conclusion

The research described trends of pollutants in Baoding with analysis of time series and made predictions on future pollutants.

Pollutant concentrations have been linked to some meteorological factors. For instance, the concentration tends to be volatile upon season factors[6].

High temperature and low wind speed are adverse for expansion of pollutants, but conductive to O3accumulation[7]. Therefore, O3is a major pollutant in summer.

In spring, O3concentration keeps lower relative to summer and it can be concluded that high illumination is a leading factor of high-concentrated O3[8].

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