## Abstract

It is common to assess the 'memory strength' of a stationary process by looking at how fast the normalized log-determinant of its covariance submatrices (i.e., entropy rate) decreases. In this work, we propose an alternative characterization in terms of the normalized trace-inverse of the covariance submatrices. We show that this sequence is monotonically non-decreasing and is constant if and only if the process is white. Furthermore, while the entropy rate is associated with one-sided prediction errors (present from past), the new measure is associated with two-sided prediction errors (present from past and future). Minimizing this measure is then used as an alternative to Burg's maximum-entropy principle for spectral estimation. We also propose a counterpart for non-stationary processes, by looking at the average trace-inverse of subsets.

Original language | English |
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Pages (from-to) | 2767-2781 |

Number of pages | 15 |

Journal | IEEE Transactions on Information Theory |

Volume | 68 |

Issue number | 4 |

DOIs | |

State | Published - 1 Apr 2022 |

## Keywords

- Maximum entropy
- causality
- minimum mean square error
- prediction