I agree, but: the technique of “singular spectrum analysis” is pretty much PCA applied to a covariance matrix resulting from time-lagging the original time seri

I agree, but: the technique of “singular spectrum analysis” is pretty much PCA applied to a covariance matrix resulting from time-lagging the original time series. (https://en.wikipedia.org/wiki/Singular_spectrum_analysis https://en.wikipedia.org/wiki/Singular_spectrum_analysis) So this is not unheard of for time series analysis.