A statistical test for the detection of AR processes corrupted by multiplicative colored noise

This paper addresses the problem of detecting the presence of colored multiplicative noise, when the information process can be modelled by a parametric AR process. A cumulant based suboptimal detector is studied, when the multiplicative noise is zero-mean. This detector tests the nullity of a specific cumulant slice. Another detector is developed, when the multiplicative noise has non-zero mean. This detector consists of filtering the data by the fitted AR filter. Higher-order cumulants of the residual data are then shown to be efficient for the detection problem.