Stationary discrete-time covariance factorization by use of Newton Raphson iteration

The solution to the problem of factorization of the covariance function of a stationary, discrete-time process is obtained by using a Newton-Raphson procedure which converges quadratically in I, provided the initial iterate is chosen suitably. The existence of a suitable initial iterate is guaranteed by an appraximation result. An application to error localization in spectral factorization is suggested.