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Adapting Marchenko–Pastur Filtering to EWMA Correlation Matrices

Article Quant Q&A · Author: NachoDR
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Summary

The document asks how to apply Marchenko–Pastur random matrix filtering to an exponentially weighted moving average (EWMA) correlation matrix. For a conventional sample matrix, it describes using the ratio of observations to variables to set an eigenvalue threshold, then asks how that ratio should change when observations receive unequal, decaying weights.

It points to a research paper on the asymptotic spectrum of the EWMA covariance estimator as a possible source for the adjustment, but does not explain the paper’s derivation or provide a formula. The note therefore identifies a practical question about eigenvalue denoising rather than offering a worked method or empirical evidence. Readers will need to consult the cited research and check its assumptions before applying a threshold to a particular EWMA estimate.

Key ideas

  • Marchenko–Pastur filtering uses an eigenvalue threshold to distinguish potentially noisy components of a sample correlation matrix.
  • The usual threshold depends on the ratio of observations to variables.
  • Exponential weighting changes the effective information in the observations and raises the question of how to adjust that ratio.
  • The document points to research on the asymptotic spectrum of EWMA covariance estimators but does not derive an adjustment.

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# How do you adapt Marcenko-Pastur for EWMA correlation matrix


# How do you adapt Marcenko-Pastur for EWMA correlation matrix












Hi to denoise the correlation matrix you can use the marcenko pastur distribution. Even without getting into its detail,. its easy, you just use t/n to get the lambda value under which you will discard eigenvalues. But how do you adapt T/N when the matrix is an expotentially weighted one?

this paper seems to have it, but its math is above my specialty: https://www.researchgate.net/publication/222925495_The_asymptotic_spectrum_of_the_EWMA_covariance_estimator

more on Marcenko https://en.wikipedia.org/wiki/Marchenko%E2%80%93Pastur_distribution

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