The interacting impact between the crude oil prices and the stock market indices in China is investigated in the present paper, and the corresponding statistical behaviors are also analyzed. The database is based on the crude oil prices of Daqing and Shengli in the 7-year period from January 2003 to December 2009 and also on the indices of SHCI, SZCI, SZPI, and SINOPEC with the same time period. A jump stochastic time effective neural network model is introduced and applied to forecast the fluctuations of the time series for the crude oil prices and the stock indices, and we study the corresponding statistical properties by comparison. The experiment analysis shows that when the price fluctuation is small, the predictive values are close to the actual values, and when the price fluctuation is large, the predictive values deviate from the actual values to some degree. Moreover, the correlation properties are studied by the detrended fluctuation analysis, and the results illustrate that there are positive correlations both in the absolute returns of actual data and predictive data.

The objective of this work is to investigate the relationships between the crude oil market and the stock market and examine whether the shocks in crude oil price transmitted to Chinese stock market will receive considerable attention from investors. In the past decade, the crude oil demand of China is growing rapidly, and China has already become the second-largest oil importer in the world, after the United States. Fourteen years ago, China from an oil-exporting country became a net oil-importing country. From then on, the movement of crude oil prices had a strong influence on the economic behavior of individuals and firms, and as a result, it affects the economic development directly. In another aspect, since July 2009, China has taken the place of Japan to be the world’s second-largest stock market, and the stock market has played an important part in its economy. China has two stock markets: Shanghai Stock Exchange and Shenzhen Stock Exchange. The indices studied in the present paper are Shanghai Composite Index (SHCI) and Shenzhen Compositional Index (SZCI). These two most influential indices play an important role in Chinese stock markets. We also consider Shenzhen Petrochemical Index (SZPI) and the stock price of China’s largest oil company: China Petroleum & Chemical Corporation (SINOPEC). Daqing oil field and Shengli oil field are the first and the second largest oil fields in China respectively, the crude oil prices of Daqing and Shengli have a strong impact on Chinese energy market. The data for these crude oil prices and indices in the 7-year period is selected and analyzed by the statistical method and the neural network method.

Recently, some progress has been made in the study of fluctuations for the financial market and the energy market in China, for example see [

In this paper, we introduce a new method: the jump stochastic time effective function in the neural network, to investigate the relationships between the crude oil market and the stock market. And the intelligent system, artificial neural networks with random theory are integrated in this work. The method is different from the methods used in previous papers [

Chinese oil market is attracting more and more attentions from all over the world. China has been the world’s second-largest oil consumer since 2003, and its oil demand reached

The output and the growth rate of crude oil in China.

In fact, China has become a net importer of crude oil since 1996; and the import dependence has exceeded

China’s crude oil import

China’s crude oil consumption

In the real crude oil market, understanding the process by which oil prices evolve is fundamental to our knowledge of this market. Many empirical evidences, like the asymmetric and leptokurtic feature of return distributions and volatilities, strongly suggested an inappropriateness for the usage of Brownian motions in the Black-Scholes model. More precisely, it is often observed that the return distribution is skewed to zero and has a higher peak and fatter tails than those of the corresponding normal distribution. To explain those empirical phenomena, many researches propose innovative models such as normal jump diffusion models (see [

There are various methods to forecast the volatilities of the time series, for example, the autoregressive conditional heteroscedasticity model has been applied by many financial analysts [

First we introduce the three-layer BP neural network model in Figure

The plot of three-layer neural network.

Obviously, the real data follow normal distribution ingeneral. However, the tail of the real distribution is fatter than the normal, which is called fat-tail phenomena. It is caused by drastic fluctuation of stock price. Moreover, we can find that the log return of stock price will fluctuate rapidly at intervals. In view of the above reality problem, the error of the output is defined as

where

Data is divided into two sections: the data from 2003 to 2007 is used for training and the rest is used for testing. For the stock indices, we input five kinds of stock prices: daily open price, daily closed price, daily highest price, daily lowest price, and daily trade volume, and one price of stock prices in the output layer: the closed price of the next trade day. And for the crude oil prices, we input five kinds of prices: the crude oil price of Brent, WTI, Dubai, Daqing, and Shengli, and the crude oil price of Daqing (or Shengli) of the next trade day is in the output layer. The number of neural nodes in input layer is 5, the number of neural nodes in the hidden layer is 13, and the number of neural nodes in output layer is 1. In this section, we take

Normalize the data as follows:

At the beginning of data processing, connective weights

Introducing the jump stochastic time effective function

Establishing an error-acceptable model and setting preset minimum error. If output error is below preset minimum error, go to Step

Modify connective weights by calculating backward for the node in output layer:

Output the predictive value.

Next, according to the computer simulations of the given neural network model, we do the comparisons between the predictive data of the model and the actual data of SHCI, SZCI, SZPI, Daqing, Shengli, and SINOPEC. And these comparison results are plotted in Figure

In Figure

Linear regression parameters.

Parameter | SHCI | SZCI | SZPI | Daqing | Shengli | SINOPEC |
---|---|---|---|---|---|---|

0.9940 | 0.9715 | 0.9107 | 0.9217 | 0.8776 | 0.9934 | |

8.5849 | 510.7603 | 91.7800 | 4.9774 | 5.6977 | 0.1957 | |

0.9806 | 0.9824 | 0.9749 | 0.9942 | 0.9941 | 0.9792 |

Comparisons of the predictive data and the actual data.

Regressions of the predictive data and the real data.

In Section

Evaluation of the prediction.

SHCI | SZCI | SZPI | Daqing | Shengli | SINOPEC | |
---|---|---|---|---|---|---|

MAE | 116.5679 | 433.4098 | 37.8812 | 2.8028 | 3.6815 | 0.4957 |

MRE | 0.0431 | 0.0448 | 0.0343 | 0.0349 | 0.0466 | 0.0448 |

Theil’s IC | 0.0269 | 0.0260 | 0.0236 | 0.0348 | 0.0367 | 0.0273 |

BP | 1.1760 | 5.6445 | 1.8592 | 4.4732 | 1.5301 | 1.5276 |

VP | 0.0496 | 0.4514 | 0.15795 | 0.0047 | 0.0045 | 7.8972 |

CP | 0.9504 | 0.5486 | 0.84205 | 0.9942 | 0.9955 | 1.0000 |

In the next part, we will discuss the relationship between the crude oil price fluctuation of Daqing and the predictive values of the model. It is apparent in Figure

The relationship between the fluctuation and the prediction by the absolute return intervals.

MAE | MRE | |
---|---|---|

0.0312 | 17.3123 | |

0.0363 | 16.4007 | |

0.0401 | 16.3452 | |

0.0387 | 14.8879 | |

0.0376 | 26.2455 | |

0.0382 | 18.2984 |

Comparisons of the fluctuation and the prediction of Daqing.

In this section, we discuss the statistical properties of SHCI, SHZI, SZPI, Daqing, Shengli, and SINOPEC in the 7-year period from January 2003 to December 2009. Figure

Returns statistics of the real data.

SHCI | SZCI | SZPI | Daqing | Shengli | SINOPEC | |
---|---|---|---|---|---|---|

Mean | 7.6353 | 1.2217 | 8.7236 | 6.8830 | 8.4244 | 1.5475 |

Variance | 3.3633 | 3.9532 | 3.6080 | 6.3243 | 7.9565 | 7.4543 |

Skewness | −0.0779 | −0.1274 | −0.3832 | −0.1276 | −0.0643 | 0.3245 |

Kurtosis | 3.1675 | 2.4920 | 2.2832 | 3.1553 | 1.8875 | 2.4495 |

Minimum | −0.0884 | −0.0932 | −0.0844 | −0.1352 | −0.1263 | −0.1030 |

Maximum | 0.0954 | 0.0963 | 0.0843 | 0.1323 | 0.1146 | 0.1015 |

Returns statistics of the predictive data.

SHCI | SZCI | SZPI | Daqing | Shengli | SINOPEC | |
---|---|---|---|---|---|---|

Mean | −9.9940 | −4.3613 | 2.2083 | −7.4974 | −2.0295 | −4.9588 |

Variance | 8.3044 | 1.1969 | 9.5615 | 1.0991 | 1.1038 | 1.2144 |

Skewness | 0.6257 | 0.0838 | 1.0189 | 0.2120 | 0.1417 | 0.5700 |

Kurtosis | 2.6270 | 2.3022 | 1.9964 | 3.1030 | 2.0811 | 1.7350 |

Minimum | −0.08211 | −0.1327 | −0.2057 | −0.1227 | −0.1101 | −0.1073 |

Maximum | 0.1525 | 0.1340 | 0.2815 | 0.1589 | 0.1250 | 0.1597 |

Returns of the indices in the 7-year period from January 2003 to December 2009.

Detrended fluctuation analysis (DFA) is a scaling analysis method providing the scaling exponent

Compute the mean

In each box, fit the integrated time series by using a polynomial function,

For a given box size

In this paper, we use DFA to analyze the absolute returns of the actual data and the predictive data, see Figure

Scaling exponent of the absolute returns.

Scaling exponent | SHCI | SZCI | SZPI | Daqing | Shengli | SINOPEC |
---|---|---|---|---|---|---|

3.5852 | 3.6523 | 3.7007 | 3.8456 | 3.9760 | 3.6342 | |

5.6438 | 5.7443 | 5.6002 | 5.9843 | 5.7712 | 5.8732 |

Detrended fluctuation analysis for the absolute returns of the actual data and the predictive data. (a) The plot of the absolute returns for the actual data from January 2003 to December 2009. (b) The plot of the absolute returns of the predictive data from January 2008 to December 2009.

In this paper, we introduce the jump stochastic time effective neural network model to forecast the fluctuations of SHCI, SZCI, SZPI, Daqing, Shengli, and SINOPEC. The corresponding statistical behaviors of these indices are investigated; and several kinds of comparisons between the actual data and the predictive data are given. Further, the absolute returns of the actual data and the predictive data are studied by the statistical method and the detrended fluctuation analysis.

The authors were supported in part by National Natural Science Foundation of China Grant nos. 70771006 and 10971010, and BJTU Foundation grant no. S11M00010.