Fitting the exogenous model to measured data

The paper deals with the problem of fitting a statistical model to observations. The proposed approach relies on modeling data as drawn from an exogenous process, namely a doubly stochastic random sequence, where a real, nonnegative process modulates a Gaussian, possibly complex, one. Approximating the modulating component by a random constant ensures that measured data can be completely specified based on a first- and second-order statistical characterization. In the following we demonstrate that ascertaining to what extent that approximation holds is paramount to solving a binary hypothesis testing problem. In particular, proper data processing leads to a distribution-free test, namely to a test statistic which is one and the same independent of the data distribution and correlation. The performance of the test has been assessed via Monte Carlo simulation: its operating characteristics show that it represents a powerful tool for achieving an accurate statistical description of real data