Markov and Non-Markov Models for Brand Switching and Market Share Forecasting

 Abstract—Markov chain has been a popular approach for the brand switching problem and market share forecasting in many industries. This paper presented four mathematical models, two existing and two new ones, developed based on different assumptions, and different focuses in the formulations. The four models include a homogeneous Markov model, a time-varying Markov model, a new extended time-varying Markov model, and a new non-Markov model. A numerical example in the telecommunication industry is included to illustrate that all four models can be applied to the brand switching problem. Although Markov models are popular, forecasters should not blindly apply them to their problems. In order to achieve the best forecasting results, forecasters should have good understand of the problems, and market conditions and trends, then make the most appropriate assumptions; and apply or even develop the most suitable models. Index Terms—Markov chain, brand switching, competition, forecasting, market share, matrix algebra.