  The Random Parameters model was proposed to explain the structure of the
covariance matrix in problems where most, but not all, of the eigenvalues of
the covariance matrix can be explained by Random Matrix Theory. In this
article, we explore other properties of the model, like the scaling of its PDF
as one take larger scales. Special attention is given to the multifractal
structure of the model time series, which revealed a scaling structure
compatible with the known stylized facts for a reasonable choice of the
parameter values.
