Dual algorithm for ARMA spectrum estimation

The present work describes an ARMA estimation aIgorithm that differs from the known available techniques. It substitutes the autocorrelation estimation sequence by the sequence of estimated reflection coefficients. These are reliably provided by the Burg technique [1]. Then it fits to the process both a sequence of higher order linear predictors (e.g., Levinson algorithm), and a sequence of higher order linear innovations filters (e.g., by recursive inversion). Finally, it obtains the MA coefficients from the linear relations satisfied by the corresponding coefficients of the successive higher order linear predictors, and likewise obtains the AR coefficients from the linear relations satisfied by the corresponding coefficients of the successive higher order innovation filters. We stress that the procedure does not use the sample autocorrelation lags; it uses instead the sequence of sample reflection coefficients, from which it estimates independently of each other and in a dual way, the MA and the AR components of the process.