Chiba Tomoaki, Hino Hideitsu, Akaho Shotaro, Murata Noboru
Department of Electrical Engineering and Bioscience, Waseda University, Shinjuku, Tokyo, Japan.
Department of Computer Science, University of Tsukuba, Tsukuba, Ibaraki, Japan.
PLoS One. 2017 Jan 11;12(1):e0169981. doi: 10.1371/journal.pone.0169981. eCollection 2017.
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.
在产品市场或股票市场中，不同的产品或股票争夺相同的消费者或购买者。我们提出了一种使用产品份额的多元时间序列来估计产品份额的时变转移矩阵的方法。该方法基于这样的假设：每个观察到的份额时间序列都是由转移概率矩阵表征的潜在马尔可夫过程的平稳分布。我们在自然假设下为每个观察估计转移概率矩阵。我们在汽车份额的真实数据集上证明，所提出的方法可以找到份额的内在转移。所得的转移矩阵揭示了有趣的现象，例如，在丰田集团销售额超过通用汽车销售额的财年中，丰田集团和通用汽车集团之间流量的变化，这是一个合理的情况。
