Spurious Dependence

We study the problem of potentially spurious attribution of dependence in moderate to large samples, where both the number of variables and length of variable observations are growing. We approach this question of double asymptotics from both theoretical and empirical perspectives. For theoretical characterization, we consider a combination of poissonization and large deviation techniques. For empirics, we simulate a large dataset of i.i.d. variables and estimate dependence as both sample size and the number of iterations grow. We represent the different effects of sample size versus length of variables, via an empirical dependence surface. Finally, we apply the empirical method to a panel of financial data, comprising daily stock returns for 60 companies. For both simulated and financial data, increasing sample size reduces dependence estimates after a certain point. However, increasing the number of variables does not appear to attenuate the potential for spurious dependence, as measured by maximal Kendall's tau.