  Driven by network intrusion detection, we propose a MultiResolution Anomaly
Detection (MRAD) method, which effectively utilizes the multiscale properties
of Internet features and network anomalies. In this paper, several theoretical
properties of the MRAD method are explored. A major new result is the
mathematical formulation of the notion that a two-scaled MRAD method has larger
power than the average power of the detection method based on the given two
scales. Test threshold is also developed. Comparisons between MRAD method and
other classical outlier detectors in time series are reported as well.
