After quick development in the past three decades, information of this rich growth journey must be included in GDP, Shenzhen economic gross statistical index, and certain periodicity and increase rule are exhibited. This rule will certainly be more obvious for the mid and long-term development potential of “13th five-year planning”. Thus according to Shenzhen GDP data for time series analysis, we use data-driven modeling method to concentrate all the factors influencing GDP growth into increase history of GDP itself, so as to fit increase history and predict development and change of GDP during the “13th five-year planning”. In the idea of data-driven modeling, all the factors influencing one variable are concentrated to this variable’s historic records.

The changes of time series can be roughly divided into superposition or combination of trend change, periodic change, cyclical fluctuation as well as random fluctuation. As a common random time series model, ARIMA model was established by Box and Jenkins, called Box-Jenkins method or B-J method jointed [17] . ARIMA model has three basic types: AR: Auto-regressive model, MA: Moving Average model and ARIMA: Auto-re- gressive Integrated Moving Average model. The advantages of the method are it not only reflects the influence of systematic factors such as continual advancement of technology, and sustainable growth of work force, continual improvement of educational level, continual formation of capital, continual improvement of total factor productivity, but also includes many unobservable factors such as change of system, climate, ideal, etc. The paper adopts ARIMA model with form as follows.

Consider series , if it can become stationary series after d times of differencing, i.e., then:, is stationary series, i.e., then ARMA(p, q) model can be established.

The ARMA (p, q) model after d order differencing is called ARIMA (p, d, q) model (Auto-regressive Integrated Moving Average Model), in which p and q are order numbers of moving average, while ε_t is a white noise process.

Local GDP is used to represent economic growth level of Shenzhen in this paper. Local GDP in Shenzhen is a monetary value index reflecting ultimate achievement of production activities of all resident units in the city in the whole year, able to deliver a comprehensive picture of total scale of economic activities in the whole society, and is an important comprehensive index to measure economic strength and evaluate economic situation in Shenzhen. For data of nominal GDP gross fails to eliminate effect of inflation, the paper takes the nominal data issued by Shenzhen Statistics Department and local GDP index number as reference to correct nominal GDP data series, and converts it to actual GDP series calculated by the price in 1979, and makes analysis according to this data series.

The growth rate of local GDP in Shenzhen refers to annual increase rate of GDP, and should be calculated by using Shenzhen total GDP calculated in comparable prices. The computing formula of actual GDP growth rate is as follows:

We obtain total local GDP in Shenzhen from 1979 to 2014 from “Shenzhen statistical yearbook”, and use time series y_t to express it. GDP growth trend diagram is made according to these data (Figure 1), which roughly shows long-term rise trend of y_t, instead of being steadily flat. The first order difference of the original GDP sequence is performed by using eviews6.0 software (Figure 2), which still roughly shows it is not steadily flat. After second order differencing, it is difficult to see whether the time series of the two order difference is stable (Figure 3), then we perform ADF unit root test on the series, and use model of inconstant term and trend term for testing, and determine lagging order number of model is 3 according to AIC rule. The test result is as shown in Table 1 and Table 2. Statistics value of second order difference ADF is 1.638473, which is greater than the critical values in three different significance levels and means that second order difference series is non-stationary. Then we go on to third order differencing (Table 2 and Figure 4). We find that ADF statistics is −3.748875, smaller than critical values in three different significance levels, then series after third order differencing is stationary. So we think difference order number d of ARIMA (p, d, q) model is equal to 3.

Then we define lagging order number p and q, ARMA (p, q) model’s order number can be judged using cutoff property of the model sample’s autocorrelation function and sample’s partial autocorrelation function. The

judgment rule is as follows: if partial correlation function of stationary time series is cutoff, while autocorrelation function is trailing, then this series is suitable for AR model; if the partial correlation function of stationary time series is trailing, while autocorrelation function is cutoff, then this series is suitable for MA model; if the partial correlation function and autocorrelation function of stationary time series are all trailing, then this series is suitable for ARMA model.

The results of autocorrelation function test to sequence D³y_t, which can be seen in Figure 5, show that the autocorrelation coefficient (AC) and the partial autocorrelation coefficient (PAC) are not stable and respectively reduce from the eighth order and sixth order. So according to the Akaike info criterion and Schwarz criterion, the value of p and q are combined for 30 groups ARIMA (p, 3, q) [p = 2, 3, 4, 5, 6; q = 3, 4, 5, 6, 7, 8] model. By constantly adjusting the order, then residual autocorrelation tests of equation, tests of goodness of fit, we try to make the model fit the best. Ultimately we take the best p, q values were 5, 7, the following ideal ARIMA (5, 3, 7) model was get. The estimated results of the model by using eviews6.0 software are as follows:

The output result of ARIMA (5, 3, 7) model (Table 3) shows that the model has high fit goodness, up to 0.90. All the parameters passed t test, p values are all lower than 0.05 (except AR (2)), and parameters are significantly different from 0. Meanwhile, the residual error series and Δ³y_t actual value and fitted value series are fitted (Figure 6). The figure shows that the change of model’s fitted values and actual values has high consistency. The diagram of autocorrelation and partial autocorrelation about first 20 orders of residual error series ε _t is made, which shows the autocorrelation function and partial autocorrelation function all fall confidence interval, and residual error series should be the white noise process. This shows Δ³y_t fitted value is unbiased estimate of actual value. The model passes test and has good fitting effect.

Based on the ARIMA model and the equation, the formula of y_t is:

Prediction over local total GDP of Shenzhen in 1987-2013 is made using ARIMA (5, 3, 7) model, and actual numerical values are used to calculate errors (Table 4). The data in Table 4 show that the predicted values are much close to actual values, and average prediction errors are calculated as 1.5%, approximating to 2 percentage points, which shows good fitting effect and higher prediction precision of the model. Thus this model can be used to predict the actual GDP of Shenzhen in “13th five-year planning” period (Table 5).

It is undeniable that any prediction of the future will have a certain error. To ensure the accuracy of the forecast as much as possible, the predicted results were limited in a certain range. According to the results and the mean prediction error from 1987 to 2014, this article takes the mean absolute error as 2% for convenient calculation, assume that the probability of the occurrence of a positive error or a native error is 1% and that the error increase 1% per year because of the dynamic prediction. The nominal GDP of Shenzhen will reach 3111 billion RMB in 2020 in the positive error and 2703.9 billion RMB in the native error. Therefore, in the benchmark scenario, the GDP of Shenzhen in 2020 should be in 2703.9 to 3111 billion RMB, with 2703.9 billion as the upper limit of the pessimistic scenario, and 3111 billion RMB as the lower limit of the optimistic scenario that year. Compared with that of the last five-year plan and the five-year plan before the last, the economic growth rate showed a falling tendency, with an average growth rate around 9.5% in the thirteenth five-year plan. And the average growth rate will be 9.5% in the thirteenth five-year plan in the positive error, 8.3% in the native error.

Based on combination of scene hypotheses about recent international, domestic and local economic development situation, we can identify several prediction schemes as shown in Figure 8. The best “optimistic” scene (quadrant I) is possible when optimistic changes occur concurrently in international, domestic and surrounding situations in Shenzhen; “mesoscopic scene”―“reference scene” (quadrant II) is possible when the international situation is pessimistic, while domestic or surrounding situation is optimistic; the worst “pessimistic” scene (quadrant III) is possible when the international situation is pessimistic, while domestic or surrounding situation is also pessimistic. “mesoscopic” scene―“reference” scene (quadrant IV) is possible when the international situation is optimistic, while domestic or surrounding situation is pessimistic. The specific scene design is as shown in Table 6.

The results shown in Table 5 indicate the possible economic development on condition that no significant changes happen in policies or external environment, namely, the effects of the economic fluctuation, the macroeconomic

policy changes or other special factors were not taken into consideration, and some main factors that influence the economic development of Shenzhen (such as the population and the labor force, natural resources, exports, technological progress, industrial structure, demand structure, total factor productivity and so on) change along the trend of the past in the analysis above. We use this as a benchmark of scenario analysis, providing comparable frame of reference to other situations. The predicted GDP for optimistic and pessimistic situations were calculated by increasing or decreasing the reference value by 2% respectively, and divided by the relevant implicit price deflator (Table 7). After error adjustment, the predicted GDP of Shenzhen from 2014 to 2020 in different situation was presented in Table 8.

After combination of previous conclusion about status quo analysis, the probability of “mesoscopic” scene is the highest, so it is taken as “reference scene” (Figure 9). Against this background, in 2016-2020, average annual rate of GDP growth is 9.5%. After error adjustment, the economic growth rate in “reference scene” is between 8.3% - 10.5%. The probability of “optimistic” or “pessimistic” scenes is relatively lower, so they are taken as sub-reference scenes. In “optimistic/best” situation, in 2016-2020, the average annual rate of GDP growth is 11.5%. After error adjustment, the economic growth rate in “optimistic scene” is between 10.5% - 12.7%. In “pessimistic/risk” scene, in 2016-2020, average annual rate of GDP growth is 7.1%. After error adjustment, in “pessimistic scene”, the economic growth rate is between 6.1% - 8.3%. Probability of other “extreme” scenes is extremely low, at two terminals of “pessimistic” scene and “optimistic” scene, and the economic growth rates are lower than 6.1% and higher than 12.7%, which is negligible.