Measures of dependence and tests of independence

Measures of dependence and resulting tests of independence are surveyed. Measures arising both from linear and nonlinear modeling are examined. Tests based on chaos theory are briefly discussed. The main emphasis, however, is on some recently developed nonparametric tests using estimated distribution and density functions. Most of the paper is phrased in terms of serial dependence for a univariate stationary time series, but it is indicated how more general situations can be analysed. The bootstrap is an essential tool for determining the critical value of the new tests.