Abstract
In this note I provide some discussion on the paper by “High-dimensional auto covariance matrices and optimal linear prediction” by T. McMurry and D. Politis.
Highlights
I congratulate Professor McMurry and Professor Politis for their important contribution to the time series prediction problem
If the covariance functions were known, the classical celebrated Wiener-Kolmogorov theory lays a beautiful foundation of the prediction problem
The covariance functions are not known, and they need to be estimated from data
Summary
I congratulate Professor McMurry and Professor Politis for their important contribution to the time series prediction problem. If the covariance functions were known, the classical celebrated Wiener-Kolmogorov theory lays a beautiful foundation of the prediction problem. One can derive various close-form expressions for the best linear predictors. The covariance functions are not known, and they need to be estimated from data.
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