Reconstructing a finite length sequence from several of its correlation lags

In this paper we present an algorithm which answers the following question: Given a finite number of correlation lags, what is the shortest length sequence which could have produced these correlations? This question is equivalent to asking for the minimum order moving average (all-zero) model which can match a given set of correlations. The algorithm applies to both the case of uniform correlations and missing lag correlations. The algorithm involves quadratic programming coupled with a new representation of the boundary of correlations derived from finite sequences in terms of the spectral decomposition of a certain class of banded Toeplitz matrices.