Estimation of some time series models using methodology of a nonlinear least squares problem

Abstract

We have considered the so-called multiple exponential-sinusoidal model. This model is defined as a sum of multiple damped exponentials and multiple damped sinusoids in noise. The problem of estimation of parameters of the model has been addressed. It has been shown that this problem can be solved as a nonlinear least squares problem whose variables separate. The problems arising in implementation of Levenberg method for estimation of „nonlinear" parameters of the model have been discussed, and some results simplifying implementation of the method in this case have been obtained.