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Autoregressive frequency detection using Regularized Least Squares

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  • Chen, Bei
  • Gel, Yulia R.

Abstract

Tracking of an unknown frequency embedded in noise is widely applied in a variety of applications. Unknown frequencies can be obtained by approximating generalized spectral density of a periodic process by an autoregressive (AR) model. The advantage is that an AR model has a simple structure and its parameters can be easily estimated iteratively, which is crucial for online (real-time) applications. Typically, the order of the AR approximation is chosen by information criteria. However, with an increase of a sample size, model order may change, which leads to re-estimation of all model parameters. We propose a new iterative procedure for frequency detection based on a regularization of an empirical information matrix. The suggested method enables to avoid the repeated model selection as well as parameter estimation steps and therefore optimize computational costs. The asymptotic properties of the proposed regularized AR (RAR) frequency estimates are derived and performance of RAR is evaluated by numerical examples.

Suggested Citation

  • Chen, Bei & Gel, Yulia R., 2010. "Autoregressive frequency detection using Regularized Least Squares," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1712-1727, August.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:7:p:1712-1727
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    References listed on IDEAS

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    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. Zhao‐Guo Chen & Ka Ho Wu & Rainer Dahlhaus, 2000. "Hidden Frequency Estimation with Data Tapers," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(2), pages 113-142, March.
    3. Ta‐Hsin Li & Benjamin Kedem, 1998. "Tracking abrupt frequency changes," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(1), pages 69-82, January.
    4. Furrer, Reinhard & Bengtsson, Thomas, 2007. "Estimation of high-dimensional prior and posterior covariance matrices in Kalman filter variants," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 227-255, February.
    5. M. S. Mackisack & D. S. Poskitt, 1990. "Some Properties Of Autoregressive Estimates For Processes With Mixed Spectra," Journal of Time Series Analysis, Wiley Blackwell, vol. 11(4), pages 325-337, July.
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    Cited by:

    1. Kaimeng Zhang & Chi Tim Ng & Myung Hwan Na, 2020. "Real time prediction of irregular periodic time series data," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(3), pages 501-511, April.

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