Estimates of standard deviation of Spearman's rank correlation coefficients with dependent observations

We consider the problem of estimating the standard deviation of the Fisher-transformed Spearman's rank correlation coefficient between two random variables X and Y when both or either of them is serially correlated. When X or Y is not i.i.d., Efron's bootstrap (EB) and the jackknife fail to capture the autocorrelation structure in the data. The circular block bootstrap (CBB) and the stationary bootstrap (SB) can be applied as alternative nonparametric resampling schemes for stationary time series. When we can assume a time series regression model, we can apply the parametric bootstrap (PB) and the bootstrap of residuals from the model (RB) to estimate the standard deviation. We compare these six methods-EB, the jackknife, CBB, SE, PB, and RB-of estimating the standard deviation, using the simulated data which have a highly correlated first order autoregression model. As we expect, the conventional bootstrap and the jackknife perform most poorly, and the PB and RB taking into account the time series model structure are the best in bias and mean squared errors. When estimating the standard deviation of the untransformed Spearman's rank correlation, we observe a very similar result.