Predictions Using Two‐State Markov Chains
Paul Aurelian Gagniuc · 2017
First, this chapter describes the method of prediction by using the transition matrix of a two-state Markov chain. Second, it also describes the notion of steady-state vector in which the Markov chain reaches the limit of prediction. Also, the chapter brings to light the long-run distribution of a Markov chain which shows the convergence toward the steady-state vector, which represents the natural path of the machine to equilibrium. The algorithm implementations are shown separately for each step. These algorithms have been used in order to make a prediction based exclusively on a sequence of observations. To understand the convergence of a Markov chain toward the steady-state vector, several cases are further considered. In the examples, two of the cases include a double stochastic matrix and the other three cases include three right stochastic matrices.