Renormalized maximum likelihood for multivariate autoregressive models. Maanan, S., Dumitrescu, B., & Giurcăneanu, C. D. In 2016 24th European Signal Processing Conference (EUSIPCO), pages 150-154, Aug, 2016.
Renormalized maximum likelihood for multivariate autoregressive models [pdf]Paper  doi  abstract   bibtex   
Renormalized maximum likelihood (RNML) is a powerful concept from information theory. We show how it can be used to derive a criterion for selecting the order of vector autoregressive (VAR) processes. We prove that RNML criterion is strongly consistent. We also demonstrate empirically its good performance for examples of VAR which have been considered in recent literature because they possess a particular type of sparsity. In our experiments, we pay a special attention to models for which the inverse spectral density matrix (ISDM) has a specific sparsity pattern. The interest on these models is motivated by the relationship between sparse structure of ISDM and the problem of inferring the conditional independence graph for multivariate time series.
@InProceedings{7760228,
  author = {S. Maanan and B. Dumitrescu and C. D. Giurcăneanu},
  booktitle = {2016 24th European Signal Processing Conference (EUSIPCO)},
  title = {Renormalized maximum likelihood for multivariate autoregressive models},
  year = {2016},
  pages = {150-154},
  abstract = {Renormalized maximum likelihood (RNML) is a powerful concept from information theory. We show how it can be used to derive a criterion for selecting the order of vector autoregressive (VAR) processes. We prove that RNML criterion is strongly consistent. We also demonstrate empirically its good performance for examples of VAR which have been considered in recent literature because they possess a particular type of sparsity. In our experiments, we pay a special attention to models for which the inverse spectral density matrix (ISDM) has a specific sparsity pattern. The interest on these models is motivated by the relationship between sparse structure of ISDM and the problem of inferring the conditional independence graph for multivariate time series.},
  keywords = {autoregressive processes;graph theory;maximum likelihood estimation;spectral analysis;conditional independence graph;ISDM;inverse spectral density matrix;vector autoregressive process;RNML;multivariate autoregressive models;renormalized maximum likelihood;Time series analysis;Covariance matrices;Maximum likelihood estimation;Reactive power;Correlation;Upper bound;Signal processing;Renormalized maximum likelihood;vector autoregressive model;order selection;maximum entropy;convex optimization},
  doi = {10.1109/EUSIPCO.2016.7760228},
  issn = {2076-1465},
  month = {Aug},
  url = {https://www.eurasip.org/proceedings/eusipco/eusipco2016/papers/1570250910.pdf},
}
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