This paper addresses the problem of estimating the parameters of a transient random process. In many applications, the absence of model for the samples leads to the impossibility to use the classical estimation theory tools. This paper develops a cost function for the case where a parametric model for the second order spectral characteristics exists. This cost function is build from the statistical properties of the signal discrete Fourier transform (DFT) when the number of samples on the signal support tends to infinity. When the DFT bins are decorrelated, this criterion has exactly the same form as the Whittle likelihood for the stationary signals case, the power spectrum being replaced by the energy spectrum. Application of this estimation framework to visibility estimation in stellar speckle interferometry is proposed to prove the efficiency of the technique.