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Today's consumer goods markets are rapidly evolving with significant growthin the number of information media as well as the number of competitiveproducts. In this environment, obtaining a quantitative grasp of heterogeneousinteractions of firms and customers, which have attracted interest ofmanagement scientists and economists, requires the analysis of extremelyhigh-dimensional data. Existing approaches in quantitative research could nothandle such data without any reliable prior knowledge nor strong assumptions.Alternatively, we propose a novel method called complex Hilbert principalcomponent analysis (CHPCA) and construct a synchronization network using Hodgedecomposition. CHPCA enables us to extract significant comovements with a timelead/delay in the data, and Hodge decomposition is useful for identifying thetime-structure of correlations. We apply this method to the Japanese beermarket data and reveal comovement of variables related to the consumer choiceprocess across multiple products. Furthermore, we find remarkable customerheterogeneity by calculating the coordinates of each customer in the spacederived from the results of CHPCA. Lastly, we discuss the policy and managerialimplications, limitations, and further development of the proposed method.

Untangling the complexity of market competition in consumer goods -A complex Hilbert PCA analysis