An exact parametric equivalent of the periodogram

A method is presented that provides the exact equivalent representation of the periodogram by means of an MA(w-1) model. This method will be compared to inferring an MA(q) model directly from the data by estimating the parameters and selecting the optimal model order. Representing the periodogram by means of an MA(n-1) model, enables the use of The Prediction Error to make an exact quantitative comparison of the periodogram to parametric spectral estimation methods. It follows that parametric methods provide better spectral estimates than the periodogram. This is explained by the fact that the periodogram is a non-selective transformation of all data, while the parametric methods discriminate between statistically significant information and noise by means of order selection.