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Information theory provides ideas for conceptualising information andmeasuring relationships between objects. It has found wide application in thesciences, but economics and finance have made surprisingly little use of it. Weshow that time series data can usefully be studied as information -- by notingthe relationship between statistical redundancy and dependence, we are able touse the results of information theory to construct a test for joint dependenceof random variables. The test is in the same spirit of those developed byRyabko and Astola (2005, 2006b,a), but differs from these in that we add extrarandomness to the original stochatic process. It uses data compression toestimate the entropy rate of a stochastic process, which allows it to measuredependence among sets of random variables, as opposed to the existingeconometric literature that uses entropy and finds itself restricted topairwise tests of dependence. We show how serial dependence may be detected inS&P500 and PSI20 stock returns over different sample periods and frequencies.We apply the test to synthetic data to judge its ability to recover knowntemporal dependence structures.

An Information-Theoretic Test for Dependence with an Application to the Temporal Structure of Stock Returns