Open AccessTime-Varying Transition Probability Matrix Estimation and Its Application to Brand Share Analysis
Author(s) -
Takamitsu Chiba,
Hideitsu Hino,
Shotaro Akaho,
Noboru Motomura
Publication year - 2017
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0169981
Subject(s) - stochastic matrix , markov chain , market share , stationary distribution , transition rate matrix , econometrics , probability distribution , transition (genetics) , multivariate statistics , random matrix , markov process , mathematics , statistics , economics , finance , physics , chemistry , quantum mechanics , gene , biochemistry , eigenvalues and eigenvectors
In a product market or stock market, different products or stocks compete for the same consumers or purchasers. We propose a method to estimate the time-varying transition matrix of the product share using a multivariate time series of the product share. The method is based on the assumption that each of the observed time series of shares is a stationary distribution of the underlying Markov processes characterized by transition probability matrices. We estimate transition probability matrices for every observation under natural assumptions. We demonstrate, on a real-world dataset of the share of automobiles, that the proposed method can find intrinsic transition of shares. The resulting transition matrices reveal interesting phenomena, for example, the change in flows between TOYOTA group and GM group for the fiscal year where TOYOTA group’s sales beat GM’s sales, which is a reasonable scenario.