  The presence of significant cross-correlations between the synchronous time
evolution of a pair of equity returns is a well-known empirical fact. The
Pearson correlation is commonly used to indicate the level of similarity in the
price changes for a given pair of stocks, but it does not measure whether other
stocks influence the relationship between them. To explore the influence of a
third stock on the relationship between two stocks, we use a partial
correlation measurement to determine the underlying relationships between
financial assets. Building on previous work, we present a statistically robust
approach to extract the underlying relationships between stocks from four
different financial markets: the United States, the United Kingdom, Japan, and
India. This methodology provides new insights into financial market dynamics
and uncovers implicit influences in play between stocks. To demonstrate the
capabilities of this methodology, we (i) quantify the influence of different
companies and, by studying market similarity across time, present new insights
into market structure and market stability, and (ii) we present a practical
application, which provides information on the how a company is influenced by
different economic sectors, and how the sectors interact with each other. These
examples demonstrate the effectiveness of this methodology in uncovering
information valuable for a range of individuals, including not only investors
and traders but also regulators and policy makers.
