A positive partial realization of time series

For a given partial covariance sequence (C
₀
, C
₁
, ..., C
_n
) and for each MA part of the ARMA modeling filter of degree n, an AR part of the ARMA modeling filter of degree n for the solution to the rational covariance extension problem is obtained by solving a nonlinear equation, which is homotopic to a nonlinear equation determining the maximum entropy AR filter.