Forecasting the Imminent Market Shares Pertinent to HTC Corporation Domestically: The Vanguard Regarding Taiwan’s Smartphone Industry

Gm (1, 1) Envelope Analysis Model

The GM (1, 1) model was first introduced in 1982 by Professor Julong Deng to analyze systems with poor information (Deng, 1982). A grey system is one in which some of the information is known and some is unknown (Lin & Yang, 2004). Any random variation in a system is treated as the variation of the grey value within a certain range, and any random process is considered a time-varying grey process by the grey system theory. Instead of using a statistical model, grey theory uses grey generating techniques such as Accumulated Generating Operation (AGO) to transform the stochastic raw data into a more regular series. Grey prediction is one of the most important components of grey system theory. It utilizes past and current known or indeterminate information to establish a grey model to extend the past information into the future so that the grey model can be used to predict future variation tendencies of the system output. The key operation in the construction of a grey model is the use of discrete time sequence data to construct an ordinary differential equation. AGO and Inverse Accumulated Generating Operation (IAGO) are the basic tools for determining the grey forecasting model. The most extensively used grey forecasting model is GM (1, 1) (Lin, Liou, & Huang, 2011). Compared to other non-analytical methods, such as neural networks and regressive analysis, the grey model has the following characteristics: (i) a small data set (i.e., 4-6 data), (ii) less computation, (iii) high precision (in small data), and (iv) the ability to adjust and correct the model (Deng, 1989).