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A generalized Levinson algorithm for covariance extension with application to multiscale autoregressive modeling

机译：协方差扩展的广义Levinson算法及其在多尺度自回归建模中的应用

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摘要

Efficient computation of extensions of banded, partially known covariance matrices is provided by the classical Levinson algorithm. One contribution of this paper is the introduction of a generalization of this algorithm that is applicable to a substantially broader class of extension problems. This generalized algorithm can compute unknown covariance elements in any order that satisfies certain graph-theoretic properties, which we describe. This flexibility, which is not provided by the classical Levinson algorithm, is then harnessed in a second contribution of this paper, the identification of a multiscale autoregressive (MAR) model for the maximum-entropy (ME) extension of a banded, partially known covariance matrix. The computational complexity of MAR model identification is an order of magnitude below that of explicitly computing a full covariance extension and is comparable to that required to build a standard autoregressive (AR) model using the classical Levinson algorithm.
机译：经典的Levinson算法可有效计算带状的，部分已知的协方差矩阵的扩展。本文的一个贡献是引入了该算法的概括，该概括适用于实质上更广泛的扩展问题。这种通用算法可以按照满足某些图论属性的任意顺序计算未知协方差元素。然后，本文的第二个贡献就是利用了经典Levinson算法无法提供的这种灵活性，即识别带状的部分已知协方差的最大熵（ME）扩展的多尺度自回归（MAR）模型。矩阵。 MAR模型识别的计算复杂度比显式计算完整协方差扩展的计算复杂度低一个数量级，并且与使用经典Levinson算法构建标准自回归（AR）模型所需的计算复杂度相比。

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