The tools of nonlinear systems analysis can be used to determine the number of effective degrees of freedom, or dimension, of a system. The algorithms for estimating the dimension appear deceptively simple, but must be applied with extreme care or a spurious dimension estimate is likely to result. We discuss various problems, and methods to overcome them, with estimating the dimension of non-stationary time series with long autocorrelation times such as AE and AL indices. Our results show that previous estimates of the dimension of AE time series were caused by long autocorrelation times and not by the dynamics of the system. Further, calculation of the largest Lyapunov exponent also gives evidence against the presence of low dimensional chaos. ¿ American Geophysical Union 1992