The potential demand of battery electric vehicle (BEV) is the base of the decision-making to the government policy formulation, enterprise manufacture capacity expansion, and charging infrastructure construction. How to predict the future amount of BEV accurately is very important to the development of BEV both in practice and in theory. The present paper tries to compare the short-term accuracy of a proposed modified Bass model and Lotka-Volterra (LV) model, by taking China’s BEV development as the case study. Using the statistics data of China’s BEV amount of 21 months from Jan 2015 to Sep 2016, we compare the simulation accuracy based on the value of mean absolute percentage error (MAPE) and discuss the forecasting capacity of the two models according to China’s government expectation. According to the MAPE value, the two models have good prediction accuracy, but the Bass model is more accurate than LV model. Bass model has only one dimension and focuses on the diffusion trend, while LV model has two dimensions and mainly describes the relationship and competing process between the two populations. In future research, the forecasting advantages of Bass model and LV model should be combined to get more accurate predicting effect.
To resolve the problem of environmental pollution and energy shortage, the development of new energy vehicles has been paid much attention. China has become one of the fastest growing markets in the world. How to predict the future amount of BEV accurately is very important to the development of BEV both in practice and in theory.
The time series model and the causal prediction method have been done on the forecasting of car ownership in the following research. Based on the GDP growth rate, Yini (2005) used the Gompertz model to analysis the future vehicle ownership in China [
Compared with Bass model, LV model has been used for predicting market share, transition of silicon wafers, technology substitution, and market competition, which seems to be a natural way of portraying the competitive struggle in a market [
Bass model is a model for the prediction of the market share of the innovation products, technology adoption, and diffusion. The core assumption of Bass model is that the adoption of innovator is independent of other members of the social system. However, the time for the adoption of the new product is influenced by the pressure of the social system, and the pressure increases with the increase of the number of people who use it earlier. The potential users are called imitator. For example, Massiania and Gohsb (2015) investigated the potential for the use of the Bass diffusion model to promote the market diffusion of electric vehicles in Germany [
The expression of Bass diffusion model is
The Bass model expresses the essence of the diffusion process with mathematical equations, which greatly simplifies the understanding of the diffusion of innovation. The basic Bass model is based on a series of important assumptions. Nonetheless, the basic Bass model does not consider the impact of marketing strategy on the diffusion of innovation products. In view of these defects, Bass added decision variables into the Bass model and proposed a generalized Bass model.
Lotka-Volterra model is a classical method to simulate natural ecosystems, especially when it is used for population ecosystem. The model and its mathematical expressions are widely applied for describing different populations competing for environment resources and the relations among them. The model can be used for predicting certain system’s change in the future and speculate certain populations’ growth or extinction.
According to the analysis of the current situation of BEV in China, it is necessary to modify the original market efficiency function
As a new innovative product, BEV, its market potential depends on the maturity of the technology of the product, the coverage of public facilities, and the amount of government subsidies. The amount of BEV ownership from Jan 2015 to Sep 2016 in China is shown in Table
The amount of BEV ownership from Jan 2015 to Sep 2016 in China.
BEV | Month |
---|---|
273927 | Jan 2015 |
279972 | Feb 2015 |
294094 | Mar 2015 |
302414 | Apr 2015 |
313270 | May 2015 |
340224 | Jun 2015 |
357062 | Jul 2015 |
375962 | Aug 2015 |
404054 | Sep 2015 |
438370 | Oct 2015 |
463034 | Nov 2015 |
583200 | Dec 2015 |
604926 | Jan 2016 |
618926 | Feb 2016 |
641862 | Mar 2016 |
673634 | Apr 2016 |
708634 | May 2016 |
752634 | Jun 2016 |
788634 | Jul 2016 |
826634 | Aug 2016 |
870634 | Sep 2016 |
Despite the fact that, currently, national and local governments are promoting the development of BEV in China, but the effectiveness of BEV is still not as expected by most consumers. In 2012, the State Council of China passed the “energy saving and new energy automotive industry development plan (2012–2020),” which mentioned that, in 2015, the battery EV and plug-in hybrid EV production and sales volume would reach 500 thousand units and in 2020 the cumulative production and sales would reach more than 5 million vehicles. Based on the plan, the maximum market potential is assumed to be 5 million units. Through iterative calculation,
Simulated result of BEV based on Bass model.
BEV (simulated data) | BEV (observed data) | Month |
---|---|---|
266568 | 273927 | Jan 2015 |
282173 | 279972 | Feb 2015 |
299006 | 294094 | Mar 2015 |
317153 | 302414 | Apr 2015 |
336704 | 313270 | May 2015 |
357755 | 340224 | Jun 2015 |
380396 | 357062 | Jul 2015 |
404730 | 375962 | Aug 2015 |
430875 | 404054 | Sep 2015 |
458946 | 438370 | Oct 2015 |
489056 | 463034 | Nov 2015 |
521320 | 583200 | Dec 2015 |
555849 | 604926 | Jan 2016 |
592753 | 618926 | Feb 2016 |
632143 | 641862 | Mar 2016 |
674127 | 673634 | Apr 2016 |
718812 | 708634 | May 2016 |
766304 | 752634 | Jun 2016 |
816705 | 788634 | Jul 2016 |
870060 | 826634 | Aug 2016 |
926463 | 870634 | Sep 2016 |
BEV and conventional car (CV) are the two most popular products in the current automotive market. Therefore, only these two kinds are discussed for forecast the future vehicle ownership in China. The LV model can be modified similar to the Bass diffusion model; the parameter
Simulated result of BEV and CV based on LV model.
BEV |
BEV |
CV |
CV |
Month |
---|---|---|---|---|
266567 | 273927 | 155969992 | 156244073 | Jan 2015 |
282173 | 279972 | 157493647 | 157634728 | Feb 2015 |
299006 | 294094 | 159052768 | 159491006 | Mar 2015 |
317153 | 302414 | 160649120 | 161151486 | Apr 2015 |
336704 | 313270 | 162284410 | 162749930 | May 2015 |
357755 | 340224 | 163960281 | 164234376 | Jun 2015 |
380396 | 357062 | 165678480 | 165486138 | Jul 2015 |
404730 | 375962 | 167440505 | 166885738 | Aug 2015 |
430875 | 404054 | 169247482 | 168608846 | Sep 2015 |
458946 | 438370 | 171100413 | 170511430 | Oct 2015 |
489056 | 463034 | 173000174 | 172683566 | Nov 2015 |
521320 | 583200 | 174947514 | 175005500 | Dec 2015 |
555849 | 604926 | 176943055 | 177373774 | Jan 2016 |
592753 | 618926 | 178987296 | 179056774 | Feb 2016 |
632143 | 641862 | 181080607 | 181473838 | Mar 2016 |
674127 | 673634 | 183223234 | 183564066 | Apr 2016 |
718812 | 708634 | 185415293 | 185621066 | May 2016 |
766304 | 752634 | 187656780 | 187648066 | Jun 2016 |
816705 | 788634 | 189947559 | 189464066 | Jul 2016 |
870060 | 826634 | 192287371 | 191497066 | Aug 2016 |
926463 | 870634 | 194675689 | 194017066 | Sep 2016 |
The mean absolute percentage error (MAPE) as shown in (
Prediction accuracy level divided by MAPE value.
MAPE% | Prediction capability |
---|---|
<10 | Highly accurate |
10–20 | Good |
20–50 | Reasonable |
>50 | Inaccurate |
As a kind of new technology products, electric vehicle has entered into the mature automobile market. Bass model is widely used in the market diffusion of a single new product, while LV model takes no less than two species into account and it is used for forecasting less frequently. In order to compare the accuracy of these two models, MAPE is used for calculating forecasting errors.
As Table
MAPE Comparison between LV and Bass model.
MAPE | |
---|---|
Bass | 4.6% |
LV | 9.1% |
After comparison of simulation accuracy comparison, the present paper gives the forecast of BEV ownership from 2017 to 2020 as shown in Table
Forecasting of BEV ownership from 2017 to 2020 based on the two models.
2017 | 2018 | 2019 | 2020 | |
---|---|---|---|---|
Bass model | 2138387 | 3325383 | 4209993 | 4674325 |
LV model | 1008591 | 1134000 | 1263081 | 1410821 |
Forecasting of BEV ownership from 2017 to 2020 based on the two models.
The Bass model only considers the time series and does not take into account the factors that affect the development of new energy vehicles. Moreover, the forecasting result needs the sustainable development of the policy and the stability of the market environment as the guarantee condition. If the industrial policy and the market environment fluctuate greatly, the forecasting result is no longer applicable. The maximum market volume is assumed to be 5 million. For the Bass model, it will be reached in 2022 while it will only reach 1.58 million for LV model in 2022.
To compare the prediction accuracy, the present paper fitted the parameters of modified Bass and the LV model. The two models have good prediction accuracy, but the Bass model is more accurate. Part of the reason is that the LV model is more complex than the Bass model, so the variance is greater when the iterative fitting of the unknown parameters, resulting in higher MAPE value. In addition, Bass model has only one dimension and focuses on the diffusion trend while LV model has two dimensions and mainly describes the relationship and competing process between the two populations. According to the MAPE value, Bass model is proved to have better simulation capacity because of the model’s precise expression.
There are still some differences between the results of the prediction and the observed formulation. On the one hand, the new energy vehicles in the Chinese market are still in the policy support phase. The growth of new energy vehicles depends largely on the amount of subsidies and the corresponding tax benefits policy. The correspondent facilities cannot dispel consumer concerns. Therefore, the existing data based on time series has strong policy relevance. On the other hand, to some extent, the new energy vehicles have technical defects. Therefore, the forecasting methods cannot adapt to the new energy vehicles after the technical improvement. After a comparative study, it is found that although the Bass model is not able to consider the external factors, but its prediction accuracy is better than the LV model.
The authors declare that they have no conflicts of interest.
This study is supported by the National Natural Science Foundation of China (51508432), the Natural Science Foundation of Hubei (2014CFB850), and the Fundamental Research Funds for the Central Universities of China (2014-IV-034).