Linear transformations and parametric spectrum analysis

A general framework for deriving and interpreting analysis and synthesis spectra of the autoregressive (AR) and moving average (MA) type is presented. Investigation of AR linear transformations of finite dimensional data records yields a set of intermediate MA techniques associated with approximation of the inverse correlation matrix R^-1. The corresponding spectrum we call a parameterized maximum likelihood method (pMLM) spectrum. Investigation of MA linear transformations yields a set of intermediate MA techniques associated with approximation of the correlation matrix R. The corresponding spectrum we call a parameterized Bartlett spectrum (pBA). Simulations on synthetic AR, MA and ARMA data sets illustrate the techniques and lead to interesting remarks concerning the use of parameterizations of R and R^-1to differentiate between data sets of AR and MA type.