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Time-Varying Transition Probability Matrix Estimation and Its Application to Brand Share Analysis

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  • Tomoaki Chiba
  • Hideitsu Hino
  • Shotaro Akaho
  • Noboru Murata

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.

Suggested Citation

  • Tomoaki Chiba & Hideitsu Hino & Shotaro Akaho & Noboru Murata, 2017. "Time-Varying Transition Probability Matrix Estimation and Its Application to Brand Share Analysis," PLOS ONE, Public Library of Science, vol. 12(1), pages 1-13, January.
    • Handle: RePEc:plo:pone00:0169981
    DOI: 10.1371/journal.pone.0169981
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    References listed on IDEAS

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    1. Robert Tibshirani & Michael Saunders & Saharon Rosset & Ji Zhu & Keith Knight, 2005. "Sparsity and smoothness via the fused lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 91-108, February.
    2. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
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    1. Yuan, Qianshun & Semba, Sherehe & Zhang, Jing & Weng, Tongfeng & Gu, Changgui & Yang, Huijie, 2021. "Multi-scale transition matrix approach to time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).

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