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The Ledoit Wolf paper "Honey, I Shrunk the Sample Covariance Matrix" presents the formulation for the shrinkage intensity parameter estimate in Appendix B.

The formula for a weighted covariance matrix is shown in the answer to this question, and an exponentially weighted covariance matrix would use weights with an exponential decay.

I am trying to calculate a exponentially weighted covariance matrix with shrinkage. I understand that the shrinkage formula will be modified so the "constant correlation model" will use the average of all pairwise weighted correlations rather than unweighted correlations, and the sample covariance matrix will now be weighted. However, I am uncertain of how the shrinkage intensity parameter estimate would be modified.

Question: How would the Ledoit Wolf shrinkage intensity parameter estimate formulation be modified for an exponentially weighted covariance matrix?

nka5we
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  • I looked at and developed a lot of different covariance shrinkage methods using a low-level language (C#) and concluded that Ledoit-Wolf by itself is adequate/appropriate, since other methods yielded little difference in results. The goal of any shrinkage method is to "nudge" the covariance matrix toward the identity matrix, and the Frobenius norm is really the only metric that has to be monitored. – wjktrs Jan 05 '24 at 05:55
  • Thanks for the response. I would like to add exponential weighting for when the recent data is more relevant than older data, which unweighted Ledoit-Wolf cannot model. With a high decay factor, the unweighted and weighted versions should be significantly different as the weighted version should mostly reflect the recent data. – nka5we Jan 08 '24 at 12:34
  • I recall seeing covariance matrix formulations in the definition of the exponential moving average. There has to be a lot of info found from a search of "exponential decay covariance matrix" or "exponentially-weighted covariance matrix." – wjktrs Jan 08 '24 at 22:07
  • So the linked question above already provides the formulation for the weighted covariance matrix, and an exponentially weighted covariance matrix simply plugs in exponential decaying weights. My question is not how to calculate a weighted covariance matrix, but rather how to calculate a weighted Ledoit-Wolf Shrunk covariance matrix. – nka5we Jan 09 '24 at 23:15
  • I don't know if that's been done. – wjktrs Jan 10 '24 at 17:50

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