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Extremely Fast Maximum Likelihood Estimation of High‐Order Autoregressive Models

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  • Daniel F. Schmidt
  • Enes Makalic

Abstract

We consider the problem of exact maximum likelihood estimation of potentially high‐order (p>50) autoregressive models. We propose an extremely fast coordinate‐wise algorithm for fitting autoregressive models. This fast algorithm exploits several properties of the negative log‐likelihood when parameterised in terms of partial autocorrelations. We consider extensions to learning a single autoregressive model from multiple time series and to the more general case of regressions with autoregressive residuals. An implementation of the coordinate‐wise descent algorithm is shown to be the orders of magnitude faster than competing algorithms and appears to be the fastest known algorithm for maximum likelihood estimation of autoregressive models.

Suggested Citation

  • Daniel F. Schmidt & Enes Makalic, 2026. "Extremely Fast Maximum Likelihood Estimation of High‐Order Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 47(4), pages 876-884, July.
    • Handle: RePEc:bla:jtsera:v:47:y:2026:i:4:p:876-884
    DOI: 10.1111/jtsa.12839
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