Step 4: Reconstruction. Where a N k is the value of principal component and e m k is the component of eigenvector in the augmented trajectory matrix X. We scale each data series according to the logarithm to ensure that all series have the same scale. The number of components is defined based on the contribution of each component to the variance of the time series. Fig 2 shows the forecast results. The trends of the BEV and PHEV sales are obtained satisfactorily, although a relatively large error is determined with regard to the monthly data.

First, the possible existence of unit roots is analysed to ensure that the model is stationary in terms of the variables used [ 51 ]. If a time series has a unit root, then the difference of the series is conducted until it is stationary. Subsequently, co-integration tests are conducted, and an error-correction term should be added. Ganger causality tests further explain the relationships [ 52 ]. Finally, the VAR model is developed and it forecasts with the recursive method.

Step 1: Unit root test.

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The stationarity, in which the mean and variance are constant and the covariance is not time dependent, is tested using the augmented Dickey—Fuller method [ 53 ]. If the data are not stationary, then the differencing process should be conducted. Step 2: Co-integration test. To verify the existence of co-integration between x t and y t , a regression is run to assess if the residual z t is stationary. If z t is stationary, then x t is co-integrated with y t.

Thus, the first-order difference of each series, lagged regression residual, and error correction should be included in the modelling procedure [ 54 ]. Step 3: Granger causality test. The causality test is conducted using an F-test on the coefficients of the x lagged values in the regression of y. It is estimated using the ordinary least square method, supposing as a seemingly unrelated regression equation [ 31 ].

Step 4: Establishing models. The lag value is determined by calculating Aikake information criterion AIC. Where y i is the observed value, and y r is the mean. The lag value is better taken when AIC is small [ 38 ]. The model comprising the time series of the EV sales and all other variables established as follows. Step 5: Predicting. First estimate the equations and obtain all coefficients with a set of history observations. Thereafter, one-month-ahead values are forecasted.

As time advances, we re-estimate the equations with the updated data and obtain the out-of-sample forecast. The selection of economic indicators, which is intended to improve the forecast of the BEV and PHEV sales, should be able to reveal a structural relationship between the EV sales and macroeconomic environment. By considering the modelling restrictions i.

The Pearson correlation coefficients is 0. Therefore it can be concluded that both Y 1 and Y 2 shows strong correlation with X 6. We calculated and normalized the value of each indicator. As showed in Fig 3 , most of the selected indicators show nonlinear patterns.

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X 1 : Consumer price index, measuring the changes in the price of a market basket of consumer goods purchased by households. X 2 : Consumer confidence index, measuring the optimism that consumers are expressing through savings and spending activities. X 3 : Producer price index, measuring the average changes in prices received by domestic producers for their output.

We scale the time series of all eight variables according to the logarithm to ensure that they have the same scale. The result of the unit root tests shows that log y 1 , log y 2 , log x 2 and log x 4 are stationary, whereas other variables are not. However, for log x 1 , log x 3 , log x 5 , and log x 6 , the plots of the first-order difference indicate stationary behaviour. Regression among time series is conducted, and the results show that no co-integration exists among the eight time series, and predictions can be made without exogenous variables.

The VAR model with error correction is constructed. The coefficients of the equation are obtained with observations to obtain the forecast result Fig 4. The result shows that the sales prediction is reasonable to be based on these indicators. As the main objective of this paper is to build and discuss two sales-forecast models for EVs, we will not cover the ARIMA model in this paper. MAPE is a computation of mean absolute error to show how close the forecasted and real values are. Where F t is the forecast value, Y t is the actual value, and n is the length of time series. In this case, the observations of the EV sales from January to December are used as sampled data for model building, and the step-ahead forecasts are conducted.

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The predicted values are compared with the actual observations from January to December For prediction models, one of the main performance measurement is precision. The SSA model indicates satisfactory results, that is, Comparing the two models from the perspective of data collection and handling, we found that SSA have lower data requirements. SSA is a kind of principal component analysis, with strong noise reduction ability. The VAR model can be used to obtain a more precise prediction.

As both economic factors and consumer preferences are considered, the forecasted results have better interpretation. However it should be noted that the value of economic factors used in VAR models are mostly collected from the Statistics Yearbooks. Thus there will always be a lag period. In summary, for emerging market like EV market in China and some other country, both univariate and multivariate forecast models yield reasonable results. Both time series indicate an apparent rising trend.

For the BEV markets, the growth trend continues to December , followed by slight fluctuations in the late and the early At the end of , a total of BEVs would be sold. The long-term trends of the EV sales are also predicted using the VAR model, with the sum of the sales for 12 months indicating the sales of the year see Fig 6. A relatively accurate understanding of the future EV market penetration in China is indicated. In particular, nearly 0. Corresponding to the strategic plan made by the government, EVs will somehow overhaul the Chinese automobile markets in the future.

However, although the predicted results may seems optimistic, the models yield a reasonable prediction of the growing trend similar conditions can be found in the studies in [ 32 ]. The predictions made by the mathematical models on solid foundation and both results either from official documents or from mathematical models are of homogeneous significance to the EV market. Penetrations of EV can lower health-impairing pollutants and greenhouse emissions, thereby providing sources of domestic employment and investment.

Sales forecast plays a prominent role in business strategy to propel penetration and generate revenues. A univariate time-series model, which depicts the accurate tendency of EV sales, can be applied easily because only a few observations are required. A multivariate model, which accounts for an improved performance in terms of predicting error, can also be used for reliable monthly and yearly forecasts.

Our results of EV sales show rising trend, corresponding with that in the U. Yet the numerical result is bigger due to the large vehicle fleets that China already has. The multivariate models result in a better forecasting performance than the univariate ones.

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Exogenous parameters that influence the sales market of the Chinese EV industry, including consumer price and confidence, producer and retailer prices, as well as the influence from fuel markets, are good predictors of the Chinese EV sales according to causality tests.

For market participants who concentrate on generating revenue, they need to focus on the variation tendency of the market demand while analysing the economic indicators. For policy makers, incentive strategies can be formulated based on the multivariate models, such as subsidies, tax adjustment, and employment encouragements. Implications to manufacturers and researchers also include the understanding of the dynamic relationship between a single market i. For the Chinese market, positive penetrations are predicted. Thus, incentive policies can be implemented. Thus, improvements made to reduce full social lifetime cost is a direct incentive for the boost of EV market, including the size and lifetime of key components i.

Diffusion of EV market is greatly influenced by customer perception and awareness. Thus, propagating the high-quality, vast-classifications as well as the great-sustainability signals will benefit the sales of EV. Besides, the penetration is directly related to travel demand, which can be estimated with economic indicators. Usually, incentive policies include the subsidy-based and the tax-based policies. The former include purchase, charging as well as maintenance subsidies. The latter are demonstrated in tax on vehicle purchase, circulation as well as electricity cost.

In the case of China, effects of policy may also be manifested directly in the vehicle fleet PHEV bus production in China has increased dramatically from to [ 58 ]. Enhancing the recharging infrastructure, and the availability of fast-charging points is another direct incentive.

Within the charging stations, the parking configurations, charger design as well as legislation contribute to its efficiency [ 17 ]. Other incentives include urban sprawl control and lane access that are specially designed for EV; free parking or electricity; exemption of emissions test; and better insurance products. Forecasting results are significant to the expanding EV industry in China.

On the one hand, short-term forecasts enhance the understanding of the changing EV market and provide a dependable foundation for market participants, such as producers, retailers, and consumers. For the participants in the Chinese EV market, corresponding strategies should be implanted to solve problems that will arise from the expanding production, inventory, and transportation. On the other hand, long-term forecasts are significant for the EV industry because of the lengthy period of time required for production processes. The results show that the VAR model is considerably suitable, which considers the effect of economic indicators, including consumer price, consumer confidence, producer price, fuel and vehicle price and Baidu data indicator that measures the tendency of the curiosity and interest of consumers on the EV market.

This study contributes to the forecast model in three aspects, namely, the modelling framework, comparison of models, and model application. Regarding the modelling framework, interpretable models that provide reasonable forecasts for a relatively niche market, such as the EV market in China, can be created, and monthly collection of data is suitable. Multivariate time-series models may better explain the future EV market than the univariate methods. The trends of sales in the next five years are also described. The results confirm a positive future for the BEV and PHEV markets in China, which correspond to what is expected in the strategic plan by the government.

Thus, policy makers and members of the EV supply chains are able to implement reasonable regulating, producing, and retailing plans. Nevertheless, our model does not account for the unobserved heterogeneous variables, such as policy and regulation. Future studies on the forecast of EV sales and model selection are expected. We are grateful for valuable suggestions for improvements from professors and students in School of Transportation, Southeast University. National Center for Biotechnology Information , U. PLoS One.

Published online May 1. Xiaosong Hu, Editor.

## 12222 Unidad de Tecnología | ESPAM MFL

Author information Article notes Copyright and License information Disclaimer. Competing Interests: The authors have declared that no competing interests exist. Conceptualization: YZ. Data curation: MZ. Formal analysis: YZ MZ. Funding acquisition: YZ. Investigation: YZ MZ.

Methodology: YZ MZ. Project administration: YZ MZ. Supervision: YZ. Validation: YZ MZ.

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Visualization: YZ MZ. Writing — original draft: YZ MZ. Received Nov 17; Accepted Apr This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

S2 Table: Economic indicators from January to December Abstract The market demand for electric vehicles EVs has increased in recent years. Introduction In China, vehicle emissions have been increased rapidly recent years. Open in a separate window. Fig 1. Vehicle sale forecast Automobile sales forecasting has received significant attention.

Table 1 Forecast results in different countries.

Country Topic Forecast results U. A forecasts model for EV. Factors affecting EV demand. EV diffusion with logit model. EV sales projections. Methodologies Multivariate time-series models may be expected to generate accurate forecasts. Time series models for sales forecast SSA model Methodology The main objective of SSA is to decompose the original series into a sum of series; thus, each component can be identified as a trend, periodic, quasi-periodic, or noise[ 49 ]. Empirical test We scale each data series according to the logarithm to ensure that all series have the same scale.

Fig 2. VAR model Methodology First, the possible existence of unit roots is analysed to ensure that the model is stationary in terms of the variables used [ 51 ]. Empirical test The selection of economic indicators, which is intended to improve the forecast of the BEV and PHEV sales, should be able to reveal a structural relationship between the EV sales and macroeconomic environment. Fig 3. Fig 4. Fig 5. Long-term sales forecast The long-term trends of the EV sales are also predicted using the VAR model, with the sum of the sales for 12 months indicating the sales of the year see Fig 6.

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Fig 6. Discussions Penetrations of EV can lower health-impairing pollutants and greenhouse emissions, thereby providing sources of domestic employment and investment. Suggested policy For the Chinese market, positive penetrations are predicted. DOCX Click here for additional data file. S2 Table Economic indicators from January to December Acknowledgments We are grateful for valuable suggestions for improvements from professors and students in School of Transportation, Southeast University.

Data Availability All relevant data are within the paper and its Supporting Information files. References 1. Development of electric vehicles use in China: A study from the perspective of life-cycle energy consumption and greenhouse gas emissions. Energy Policy. Company BP. BP statistical review of world energy. London England British Petroleum Company; Spatial planning of public charging points using multi-dimensional analysis of early adopters of electric vehicles for a city region.