The geomagnetic activity of the <i>D<sub>st</sub></i> index is analyzed using wavelet transforms and it is shown that the <i>D<sub>st</sub></i> index possesses properties associated with self-affine fractals. For example, the power spectral density obeys a power-law dependence on frequency, and therefore the <i>D<sub>st</sub></i> index can be viewed as a self-affine fractal dynamic process. In fact, the behaviour of the <i>D<sub>st</sub></i> index, with a Hurst exponent <i>H</i>≈0.5 (power-law exponent β≈2) at high frequency, is similar to that of Brownian motion. Therefore, the dynamical invariants of the <i>D<sub>st</sub></i> index may be described by a potential Brownian motion model. Characterization of the geomagnetic activity has been studied by analysing the geomagnetic field using a wavelet covariance technique. The wavelet covariance exponent provides a direct effective measure of the strength of persistence of the <i>D<sub>st</sub></i> index. One of the advantages of wavelet analysis is that many inherent problems encountered in Fourier transform methods, such as windowing and detrending, are not necessary.