The Evolution of Grey Forecasting and its Application on Stock Price Prediction

Since Grey theory proposed by Prof. Deng [1], it has been widely applied in many fields. The traditional grey forecasting model, which is termed GM (1, 1), starts from accumulation of raw data to form a simple monotonic series. Based on this new series, the coefficients of discretilization of first order ordinary differential equation (ODE) could be solved by least square method. Then, these coefficients could be substituted into the particular solution of ODE to serve as a predictor. The solution procedure could be found in textbook.


Introduction
Since Grey theory proposed by Prof. Deng [1], it has been widely applied in many fields.The traditional grey forecasting model, which is termed GM (1,1), starts from accumulation of raw data to form a simple monotonic series.Based on this new series, the coefficients of discretilization of first order ordinary differential equation (ODE) could be solved by least square method.Then, these coefficients could be substituted into the particular solution of ODE to serve as a predictor.The solution procedure could be found in textbook [2].

Development of Grey Forecasting
The forecasting precision of GM (1, 1) is satisfactory in many cases.In order to improve its application in various situations, like drastic change data, cyclic data and seasonal change data.Recent publications concentrated on:

A) Topic (1): Different selection of initial condition
Traditional GM (1, 1) used the first raw data to serve as initial condition.Some studies found that second or third data could also be served as initial condition to enhance the forecasting precision.

B) Topic (2): The discussion of background value. [3]
The background value was set to 0.5 by Prof. Deng.Generally speaking, it is within the range 0~1.Proper selection of background value by soft computing method or computer program could increase the forecasting precision.

C) Topic (3): The improvement of original differential equation. [4]
The GM (1, 1) is linear equation which fits smooth change data.Nonlinear equation is adopted to fit drastic change raw data.The Bernoulli equation is proposed to modify the traditional model which is termed NGBM.Therefore, GM (1, 1) and Grey-Verhulst become the special cases of NGBM.Furthermore, NGBM together with changing background value which is termed as NNGBM [5] increase the forecasting precision by combination of topic ( 2) and (3).

Consideration of Grey Theory on Stock Market
The evolution and development of grey theory are still going on to achieve better results.The application of grey forecasting on the stock market was popular [5,[9][10][11][12][13].The following points were proposed to attract the attention when apply grey theory on stock price forecasting.
(1) The unchanged price The closing price could be unchanged and this will make singular phenomenon happen.Chen and Huang [14] proposed solution and it should be noticed when treat the raw data.
(2) The up or bottom price limit of day trade.
In order to avoid uncontrollable price fluctuation, the stock exchange of developing country usually regulates the up or bottom price limit of day trade.But this will affect the forecasting result when forecasted price exceed this limit.
(3) The increment of stock price is discontinuous.
The minimum changing unit is called tick.When stock price falls within different price range, the unit for tick is also different.Therefore, it should be considered.

Conclusion
Grey theory has widely applied in management and engineering and achieve satisfactory results.We all believe grey theory could apply successfully in the field of stock market forecasting.But the proposed three points above should be considered to achieve higher and better forecasting performance.