Echo State Network k-fold cross-validation can be implemented with O(Nr^2 T + k Nr^3) time, so the dominant training cost stays constant in k for long time series.
A note on the validity of cross-validation for evaluating autoregressive time series prediction.Computational Statistics & Data Analysis , 120:70–83, 2018
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Efficient Cross-Validation of Echo State Networks
Echo State Network k-fold cross-validation can be implemented with O(Nr^2 T + k Nr^3) time, so the dominant training cost stays constant in k for long time series.