Application of GM (1, N)-Markov Model in Shanghai Composite Index Prediction
In order to overcome the limitations of little used information and low accuracy for single stock market prediction model and the limitations of exponential trend for GM(1,1)-Markov combination forecast model, GM(1, N)-Markov model is suggested in this pa
- PDF / 177,491 Bytes
- 11 Pages / 439.36 x 666.15 pts Page_size
- 13 Downloads / 180 Views
Application of GM (1, N)-Markov Model in Shanghai Composite Index Prediction Wan-cai Yang, Xin-qian Wu, Er-xin Zhang, and Guang Zhu
Abstract In order to overcome the limitations of little used information and low accuracy for single stock market prediction model and the limitations of exponential trend for GM(1,1)-Markov combination forecast model, GM(1, N)-Markov model is suggested in this paper. Positive analysis is done for Shanghai composite index (monthly closing price). The results show that the established GM (1, 3)-Markov model outperforms the GM (1, 1) model and the GM (1, 1)-Markov model. Keywords Combination forecast • GM (1, N) • Markov chain • Shanghai composite index
59.1 Introduction With the development of social economy, stock has become an important tool for people to invest and manage finance. Stock market can be regarded as a grey system, in which some information is known and other information is unknown. But grey forecast is suitable for some objects with short time, a few data, little volatility and long-term tendency, and its forecast tendency is a smooth curve. For some data sequences with large stochastic volatility, the grey system usually gives bad fitting and low forecast accuracy. Note that transition probability matrix in Markov chain theory can reflect the influence extent of stochastic factors, and is suitable for dynamic process with large stochastic volatility. It can remedy the limitation of grey forecast. At the same time, grey system can remedy the weaknesses of un-follow-up effect and stationary which are used in Markov chain. If a grey system model is used
W. Yang () • X. Wu • E. Zhang • G. Zhu School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, People’s Republic of China e-mail: [email protected] E. Qi et al. (eds.), The 19th International Conference on Industrial Engineering and Engineering Management, DOI 10.1007/978-3-642-37270-4 59, © Springer-Verlag Berlin Heidelberg 2013
625
626
W. Yang et al.
to fit data and find its change tendency, the limitation of Markov forecast can be amended, see Tang et al. (2007). Thus, Combining grey system model with Markov chain has attracted much attention. At present, the popular combination model is GM (1, 1)-Markov model (Tang et al. 2007; Chen and Duan 2002; Tao et al. 2007; Li et al. 2007a, b; Liu et al. 2012; Liu 2011). However, GM (1, 1)-Markov model often gives the result of exponential growth tendency, which fails to reflect the true dynamic characteristic of some real data. In this paper, GM (1, 1)-Markov model is extended to GM (1, N)-Markov model by adding some related influent factors. An application to Shanghai composite index (monthly closing price) is also analyzed.
59.2 GM (1, N)-Markov Model 59.2.1 GM (1, N) Model Let .0/ .0/ .0/ .0/ X1 D x1 .1/; x1 .2/; x1 .n/ be a sequence of system characteristic data. While 8 .0/ .0/ .0/ .0/ ˆ X D x .1/; x .2/; x .n/ ˆ 2 2 2 2 ˆ ˆ ˆ ˆ < X .0/ D x .0/ .1/; x .0/ .2/; x .0/ .n/ 3 3 3 3 : ˆ :: ˆ ˆ ˆ ˆ ˆ
Data Loading...
