Why it is a question
THEORY-818 reports what Chorin and Lu (LIT-1304, read in NOTE-1028) measured: on Lorenz 96 with no gap of time scales, a NARMAX closure with one or two lags reproduces x₁’s statistics and doubles the forecast lead time at δ = 0.05. Its model structure was chosen “by trial and error” against the long-run mean and autocorrelation, which are among the statistics then reported, and the forecast comparison is read from plotted curves. The result is in-sample in its selection. Whether a short discrete memory still suffices when the structure is fixed before scoring is open.
What would answer it
A rerun of the two-scale Lorenz 96 test at the paper’s parameters (ε = 0.5, K = 18, J = 20, F = 10, h_x = −1, h_y = 1), by the record or another group, that fits the discrepancy NARMAX with a structure chosen by a rule fixed before scoring, and reports the Kolmogorov–Smirnov distance of x₁ and the lead time at anomaly correlation 0.6 against the full system and against the polynomial-plus-AR(1) closure, at δ = 0.05 at least. A rerun whose model orders were tuned on the scored statistics, or a comparison read off figures, does not settle it.