TY - JOUR
T1 - Time-varying transition probability matrix estimation and its application to brand share analysis
AU - Chiba, Tomoaki
AU - Hino, Hideitsu
AU - Akaho, Shotaro
AU - Murata, Noboru
N1 - Funding Information:
This work was supported by JSPS KAKENHI Grant Numbers 25120009, 25120011, and 16K16108. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
PY - 2017/1
Y1 - 2017/1
N2 - 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.
AB - 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.
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U2 - 10.1371/journal.pone.0169981
DO - 10.1371/journal.pone.0169981
M3 - Article
C2 - 28076383
AN - SCOPUS:85009067250
VL - 12
JO - PLoS One
JF - PLoS One
SN - 1932-6203
IS - 1
M1 - e0169981
ER -