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

TL;DR

This paper introduces a novel complex Hilbert PCA method to analyze high-dimensional consumer goods market data, revealing intricate firm-customer interactions and heterogeneity in consumer behavior.

Contribution

The paper develops CHPCA and Hodge decomposition techniques to extract and interpret complex, time-lagged correlations in high-dimensional market data, advancing quantitative analysis methods.

Findings

Identified significant comovements in consumer choice variables.

Revealed customer heterogeneity through coordinate analysis.

Provided policy and managerial insights based on data analysis.

Abstract

Today's consumer goods markets are rapidly evolving with significant growth in the number of information media as well as the number of competitive products. In this environment, obtaining a quantitative grasp of heterogeneous interactions of firms and customers, which have attracted interest of management scientists and economists, requires the analysis of extremely high-dimensional data. Existing approaches in quantitative research could not handle such data without any reliable prior knowledge nor strong assumptions. Alternatively, we propose a novel method called complex Hilbert principal component analysis (CHPCA) and construct a synchronization network using Hodge decomposition. CHPCA enables us to extract significant comovements with a time lead/delay in the data, and Hodge decomposition is useful for identifying the time-structure of correlations. We apply this method to the Japanese beer market data and reveal comovement of variables related to the consumer choice process across multiple products. Furthermore, we find remarkable customer heterogeneity by calculating the coordinates of each customer in the space derived from the results of CHPCA. Lastly, we discuss the policy and managerial implications, limitations, and further development of the proposed method.