Selected Applications of Grey Models in Stock Price Prediction

Introduction

Portfolio management represents a process of managing money (Fabozzi and Pachamanova, 2016), in which several issues and steps need to be defined. These include defining the investor’s preferences, goals and limitations; knowing to evaluate financial products and market conditions; constructing the investment portfolio and a trading strategy which will ensure the achievement of the mentioned goals; and finally, evaluation of the performance of such investment strategies (Fabozzi and Markowitz, 2011). It is obvious that knowledge in many different fields is needed so that successful portfolio management can be conducted over time. This is especially true when it comes to quantitative modeling. Many different mathematical and statistical models and methods have been developed over the decades in order to answer specific questions in the area of portfolio management. Since the area of quantitative finance which consists of different models, techniques and approaches has been expanding rapidly, several attempts have been made to classify and categorize them (Granger, 1989; Taylor and Allen, 1992; Ho et al. 2002; Wallis, 2011): econometric approach such as autoregressive integrated moving average, generalized autoregressive conditional heteroskedasticity (AR(I)MA-GARCH), extreme value theory (EVT), non-parametric approaches such as data envelopment analysis (DEA), multiple criteria decision model (MCDM) and other related areas within the operations research (OR), neural networks, etc. All of the approaches have their advantages and shortfalls (for discussion, please see Jo, 2003; Liu et al., 2012; Khuman et al., 2014). The majority of the methodologies are used for forecasting purposes. In order to do so, a mathematical model is needed which is used to try to make accurate predictions (Kayacan et al., 2010).

Since the interest of quantitative modeling within the portfolio management is growing, it is not surprising that the methodological approaches are evolving, combining ideas and concepts from other approaches and that relatively unknown methodologies are emerging in the literature as well. One approach which is relatively unknown compared to some usual econometric approaches of modeling stock price, return and risk is the Grey Systems Theory (GST). This theory has been in development since the 1980s in the Far East (Lin et al., 2005; Liu et al., 2016; Yin, 2013). GST consists of different models and methods which can be used in the area of decision-making under uncertainties, i.e. when the data is “grey”. The term “grey” data means that not all information is available for the decision-maker, due to ambiguity, information distortion, etc. This methodology is very appropriate for portfolio management, as many problems arise here due to data uncertainty. Investors often have to make certain decisions without full data available. Although much data and information on the stock markets are available on a daily basis, there is a lot of “grey” data that needs to be modeled adequately. It is not surprising that the research interest in GST applications on stock markets has grown in the last decade. There exist both theoretical and practical papers which deal with GST models and their usefulness on the stock market (Rathnayaka et al., 2016).