The Wiener Theory of Causal Linear Prediction Is Not Effective

Holger Boche, Volker Pohl, H. Vincent Poor

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, it will be shown that the minimum mean square error (MMSE) for predicting a stationary stochas-tic time series from its past observations is not generally Turing computable, even if the spectral density of the stochastic process is differentiable with a computable first derivative. This implies that for any approximation sequence that converges to the MMSE there does not exist an algorithmic stopping criterion that guarantees that the computed approximation is sufficiently close to the true value of the MMSE. Furthermore, it will be shown that under the same conditions on the spectral density, it is also the case that coefficients of the optimal prediction filter are not generally Turing computable.

Original languageEnglish (US)
Title of host publication2023 62nd IEEE Conference on Decision and Control, CDC 2023
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages8229-8234
Number of pages6
ISBN (Electronic)9798350301243
DOIs
StatePublished - 2023
Externally publishedYes
Event62nd IEEE Conference on Decision and Control, CDC 2023 - Singapore, Singapore
Duration: Dec 13 2023Dec 15 2023

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370

Conference

Conference62nd IEEE Conference on Decision and Control, CDC 2023
Country/TerritorySingapore
CitySingapore
Period12/13/2312/15/23

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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