AbstractIn this paper, we consider a generalized approach which is flexibly applicable to testing Granger causality in various moments and in both the full‐sample and out‐of‐sample contexts. We further use this approach to establish a class of cross‐correlation tests for financial time series analysis, and show the advantages of this class of tests in unifying and generalizing Box–Pierce‐type Granger causality tests. We also conduct a Monte Carlo simulation to show the validity of our tests, and provide an empirical example to demonstrate the flexibility of our tests in exploring various types of Granger causality.