Correlation matching by finite length sequences

The problem of matching a finite length data sequence to a set of (not necessarily uniformly spaced) correlation lags is considered. A characterization of the set of correlations that can be derived from sequences of a given length is presented. Using this characterization, an algorithm called the expanding hull algorithm is presented for determining the minimum sequence length, and a sequence of this length, which matches a given set of correlation values, is obtained. This sequence has a Z transform which is the lowest-order correlation matching moving average model. The sequence also generates the minimum length correlation extension. The expanding hull algorithm also provides a method for extendibility testing of missing lag and multidimensional correlation sequences. Numerical examples are provided.<>