^{1}

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In the paper, based on the data of Shanghai and Shenzhen 300 stock index in 2011, the
*ARIMA* model was established by using Eviews 6, and the historical trend of stock price was found out. The model was used to provide a reference for the investors.

Stock in the trading market as a trading object, with the same goods, has their own market and market prices. Because of the stock price to be affected by many factors such as company management, supply and demand, bank interest rate, public psychology and so on, it has a lot of uncertainty.

Shanghai and Shenzhen 300 index is a stock exchange in Shanghai and Shenzhen Stock Exchange in April 8, 2005 to reflect the overall trend of the stock market index A. Shanghai and Shenzhen 300 index sample covering the Shanghai and Shenzhen stock market around 60% of the market value, with good market representation and investment. The goal of Shanghai and Shenzhen 300 index is to reflect the profile and operation status of Chinese stock market stock price changes, and as the criteria for the evaluation of the investment performance, the index of investment and index derivative product innovation to provide basic conditions. So it is necessary for us to find a way to predict the stock price. In recent years, there have been papers investigating the problem (see [

By 2011, the Shanghai and Shenzhen 300 stock index of 242 data (Due to the holidays, the stock market halted, some months of data is relatively few) as a time series analysis, a prediction model is established which is used in the modeling of 234 data and the prediction of the model is based on the following 8 data. Data comes from the financial research database (RESSETDB) (see Attached Table).

The original data into a line chart was draw. A sequence of Y was written, as shown in

In order to reduce the fluctuation of the sequence, the natural logarithm transformation of the original data is still showing obvious non-stationary, so it is necessary to carry on the differential operation to the data, until after the two order difference, the sequence is obviously smooth. The two order difference is shown in

Autocorrelation function and partial autocorrelation function are the most important tools for the identification of

From

We can judge the type of time series model more accurately according to the principle of the model [

From the table can be seen as the 1 step truncation, but after 6 steps are not censored, can think the tail, which belongs to

In order to determine the order number of the model, the

m | 1 | 2 | 3 | … | … |
---|---|---|---|---|---|

0.084170 | 0.084467 | 0.084467 | … | … | |

To meet the conditions of proportion p | 13/15 = 0.87 | 13/15 = 0.87 | 14/15 = 0.93 | … | … |

n | 1 | 2 | 3 | … | 6 |

To meet the conditions of proportion p | 10/15 = 0.67 | 9/15 = 0.60 | 10/15 = 0.67 | … | 6/15 = 0.446 |

Adjusted R^{2}, AIC, SC, such as

In regression analysis, the requirement for the level of parameter t test is not so strict as the regression equation, and more is considered the whole fitting effect of the model. Adjusted R^{2}, AIC, SC are important criteria for the selection of models. And the three roots are within the unit circle, to meet the requirements. According to the standard function method, AIC, SC value reaches minimum is the best model order, so we choose

We should further verify the suitability of the model, that is, the residual sequence of the model is tested by white noise. The use of Eviews software for the chi square test, the test results are shown in

1 | 2 | 3 | |
---|---|---|---|

Adjusted R^{2} | 0.524603 | 0.524656 | 0.523013 |

AIC | −5.826493 | −5.82246 | −5.81489 |

SC | −5.811990 | −5.79346 | −5.77138 |

In

The model is suitable for the test, can be used for short-term prediction. In order to test the predictive effect of the model, we set aside the last 8 observations in December as the reference object. After the operation of the software, the result of the equation is obtained. The main contents are shown in

The inverted root of the polynomial in

Experimental results show the absolute error of the model and the percentage of absolute error are controlled within a certain range. So the fitting effect of the model is good, and the predictive value is close to the actual value.

According to

Variable | Coefficient | Std. Error | t-Statistic | Prob. |
---|---|---|---|---|

−0.988651 | 0.007213 | −137.0736 | 0.0000 | |

R-squared | 0.524603 | Mean dependent var. | 7.97E−05 | |

Adjusted R-squared | 0.524603 | S.D. dependent var. | 0.019016 | |

S.E. of regression | 0.013112 | Akaike info criterion | −5.826493 | |

Sum squared residual | 0.041087 | Schwarz criterion | −5.811990 | |

Log likelihood | 700.1792 | Hannan-Quinn criter. | −5.820650 | |

Durbin-Watson statistic | 2.127480 | |||

Inverted MA roots | 0.99 |

Time | Real value | Predictive value | Error | Error ratio (%) |
---|---|---|---|---|

1 | 2339.1 | 2372.733 | 33.633 | 1.44% |

2 | 2341.3 | 2368.373 | 27.073 | 1.16% |

3 | 2359.2 | 2364.022 | 4.8222 | 0.20% |

4 | 2335.7 | 2359.679 | 23.979 | 1.03% |

5 | 2305 | 2355.344 | 50.344 | 2.18% |

6 | 2307.9 | 2351.016 | 43.116 | 1.87% |

7 | 2311.4 | 2346.697 | 35.297 | 1.53% |

8 | 2345.7 | 2342.386 | −3.314 | −0.14% |

can represent the trend of stock price in a certain degree.

Qinghai Nationalities University Natural Science Foundation Item Number 2015XJZ03.

Shichang Shen,Yue Shen, (2016) ARIMA Model in the Application of Shanghai and Shenzhen Stock Index. Applied Mathematics,07,171-176. doi: 10.4236/am.2016.73016