title: Time-Varying Transition Probability Matrix Estimation and Its Application to Brand Share Analysis.
abstract: 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.
authors.affiliation: Department of Electrical Engineering and Bioscience, Waseda University, Shinjuku, Tokyo, Japan.
authors.forename: Tomoaki
authors.initials: T
authors.lastname: Chiba
authors.affiliation: Department of Computer Science, University of Tsukuba, Tsukuba, Ibaraki, Japan.
authors.forename: Hideitsu
authors.identifier: http://orcid.org/0000-0002-6405-4361
authors.initials: H
authors.lastname: Hino
authors.affiliation: Mathematical Neuroinformatics Group, National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki, Japan.
authors.forename: Shotaro
authors.initials: S
authors.lastname: Akaho
authors.affiliation: Department of Electrical Engineering and Bioscience, Waseda University, Shinjuku, Tokyo, Japan.
authors.forename: Noboru
authors.initials: N
authors.lastname: Murata
mesh_terms: D000465:Algorithms; D001336:Automobiles / Q000191:economics / Q000706:statistics & numerical data; D003132:Commerce / Q000706:statistics & numerical data*; D003258:Consumer Behavior / Q000706:statistics & numerical data*; D006801:Humans; D008390:Markov Chains; D011336:Probability; D013223:Statistics as Topic / Q000379:methods*; D013997:Time Factors