We present the broad-band noise structure of Anomalous X-Ray Pulsars (AXPs) and Soft Gamma Repeaters (SGRs) in the 2-60 keV energy band which are thought to be powered by either magnetic decay(Thompson & Duncan 1995) or accretion (Alpar 2001). We have used Rossi X-ray Timing Explorer (R-XTE) PCA archival light curves and derived time series for 4 AXPs and 1 SGR. We detect that AXP and SGR sources show band limited noise at low frequencies in the range 0.005-0.05 Hz. We find that this noise level can be associated with their bursts, glitches or flaring activities. We discover band-limited red noise in 1E 2259+586 only for about two years after its outburst and the associated glitch. The system shows no broad-band noise otherwise. The other three AXPs indicate a lower band-limited noise level in comparison with 1E 2259+586 and it is persistent, but show variations. We favour a model where this broad-band noise particularly as detected in 1E 2259+586 is related to the Compton scattering of thermal photons in the magnetar corona and thus reveal coronal time scales and activity.