Dataset Information

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.

SUBMITTER: Chiba T

PROVIDER: S-EPMC5226793 | biostudies-literature | 2017

REPOSITORIES: biostudies-literature

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Publications

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

Chiba Tomoaki T Hino Hideitsu H Akaho Shotaro S Murata Noboru N

PloS one 20170111 1

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 f ...[more]

PMID: 28076383

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Project description:The central nervous system (CNS) controls the limb movement by modulating multiple skeletal muscles with synergistic modules and neural oscillations with different frequencies between the activated muscles. Several researchers have found intermuscular coherence existing within the synergistic muscle pairs, and pointed out that the intermuscular synchronization existed when functional forces were generated. However, few studies involved the time-varying characteristics of the intermuscular coherence in each synergy module though all activated muscles keep in a dynamic and varying process. Therefore, this study aims to explore the time-varying coherence amongst synergistic muscles during movements based on the combination of the non-negative matrix factorization (NMF) method and the time-frequency coherence (TFC) method. We applied these methods into the electromyogram (EMG) signals recorded from eight muscles involved in the sequence of the wrist movements [wrist flexion (WF), wrist flexion transmission to wrist extension (MC) and wrist extension (WE)] in 12 healthy people. The results showed three synergistic flexor pairs (FCR-PL, FCR-FDS, and PL-FDS) in the WF stage and three extensor pairs (ECU-ECR, ECU-B, and ECR-B) in both MC and WE stages. Further analysis showed intermuscular coherence between each pairwise synergistic muscles. The intermuscular coherence between the flexor muscle pairs was mainly observed in the beta band (15-35 Hz) during the WF stage, and that amongst the extensor muscle pairs was also observed in the beta band during the WE stage. However, the intermuscular coherence between the extensor muscle pairs mainly on gamma band during the MC stage. Additionally, compared to the flexor muscle pairs, the intermuscular coherence of the extensor muscle pairs were lower in the WF stage, and higher in both MC and WE stages. These results demonstrated the time-varying mechanisms of the synergistic modulation and synchronous oscillation in motor-control system. This study contributes to expanded researches for motor control.

Dataset Information

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

Publications

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

Similar Datasets

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