Fitting ARMA Time Series Models without Identification: A Proximal Approach

Yin Liu, Sam Davanloo Tajbakhsh
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:3835-3843, 2024.

Abstract

Fitting autoregressive moving average (ARMA) time series models requires model identification before parameter estimation. Model identification involves determining the order of the autoregressive and moving average components which is generally performed by inspection of the autocorrelation and partial autocorrelation functions or other offline methods. In this work, we regularize the parameter estimation optimization problem with a non-smooth hierarchical sparsity-inducing penalty based on two path graphs that allow performing model identification and parameter estimation simultaneously. A proximal block coordinate descent algorithm is then proposed to solve the underlying optimization problem efficiently. The resulting model satisfies the required stationarity and invertibility conditions for ARMA models. Numerical results supporting the proposed method are also presented.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-liu24e, title = {Fitting {ARMA} Time Series Models without Identification: A Proximal Approach}, author = {Liu, Yin and Davanloo Tajbakhsh, Sam}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {3835--3843}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/liu24e/liu24e.pdf}, url = {https://proceedings.mlr.press/v238/liu24e.html}, abstract = {Fitting autoregressive moving average (ARMA) time series models requires model identification before parameter estimation. Model identification involves determining the order of the autoregressive and moving average components which is generally performed by inspection of the autocorrelation and partial autocorrelation functions or other offline methods. In this work, we regularize the parameter estimation optimization problem with a non-smooth hierarchical sparsity-inducing penalty based on two path graphs that allow performing model identification and parameter estimation simultaneously. A proximal block coordinate descent algorithm is then proposed to solve the underlying optimization problem efficiently. The resulting model satisfies the required stationarity and invertibility conditions for ARMA models. Numerical results supporting the proposed method are also presented.} }
Endnote
%0 Conference Paper %T Fitting ARMA Time Series Models without Identification: A Proximal Approach %A Yin Liu %A Sam Davanloo Tajbakhsh %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-liu24e %I PMLR %P 3835--3843 %U https://proceedings.mlr.press/v238/liu24e.html %V 238 %X Fitting autoregressive moving average (ARMA) time series models requires model identification before parameter estimation. Model identification involves determining the order of the autoregressive and moving average components which is generally performed by inspection of the autocorrelation and partial autocorrelation functions or other offline methods. In this work, we regularize the parameter estimation optimization problem with a non-smooth hierarchical sparsity-inducing penalty based on two path graphs that allow performing model identification and parameter estimation simultaneously. A proximal block coordinate descent algorithm is then proposed to solve the underlying optimization problem efficiently. The resulting model satisfies the required stationarity and invertibility conditions for ARMA models. Numerical results supporting the proposed method are also presented.
APA
Liu, Y. & Davanloo Tajbakhsh, S.. (2024). Fitting ARMA Time Series Models without Identification: A Proximal Approach. Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:3835-3843 Available from https://proceedings.mlr.press/v238/liu24e.html.

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