Spectral Predictability Score

• Spectral Predictability Score is a family of metrics that quantify intrinsic regularity by mapping spectral features—such as Fourier, multifractal, and singular-value spectra—into forecastability scores.
• For univariate time series, it uses FFT-based entropy measures to reveal concentrated periodicities or noise-like flat spectra, directly correlating with predictive accuracy.
• In fields like finance, climate, and recommender systems, various spectral constructs demonstrate practical applications in anticipating shifts and assessing model stability under perturbations.

Searching arXiv for the cited papers and related usage of “spectral predictability score” to ground the article in current literature. The literature suggests that spectral predictability score is not a single canonical statistic but a family of spectral or structure-based quantities used to quantify intrinsic predictability, usually before full model development or independently of a particular predictor. Across recent work, the common objective is to summarize how much exploitable regularity is present in a signal, a matrix, or a stochastic dynamical system: concentrated Fourier energy, wide or structured multifractal spectra, stable singular subspaces under perturbation, preserved forecast power across frequencies, or slow mixing in a Markov chain all serve as proxies for greater predictability (Wang et al., 17 Jul 2025, Fu et al., 2018, Valderrama et al., 2024, Simon et al., 18 Apr 2025, Mostafavi et al., 2024).

1. Scope of the term across research areas

The term appears in several technically distinct settings. In some papers it denotes a scalar score computed directly from data; in others it denotes a composite predictor, a spectral diagnostic, or a spectral upper bound on forecast informativeness. Taken together, these usages indicate a methodological family rather than a standardized benchmark.

Domain	Quantity called or used as spectral predictability score	Core mechanism
Univariate time series	$\Omega(y)=1-\dfrac{H_a(y)}{\log_a(2\pi)}$	Entropy of normalized PSD (Wang et al., 17 Jul 2025)
High-frequency equity returns	$\Delta\alpha$ or $$S_t=\omega_1\Delta\alpha_t+\omega_2\Delta f_t+\omega_3 B_t$$	MF-DFA singularity spectrum (Fu et al., 2018)
Stock-market harmonic analysis	$S=\sum_{k=1}^{K} w_k A(f_{(k)})$	Sum of dominant harmonic amplitudes (Romana et al., 2023)
Chaotic climate dynamics	$$\mathrm{SPS}(\epsilon)= (\lambda/f_0)[\ln(1/\epsilon)]^{1/\beta}$$	Spectral tail shape plus Lyapunov scale (Bershadskii, 2018)
Recommender systems	$$\mathrm{SPS}=1-\mathrm{RMSE}_{\mathrm{SPS}}/(\max-\min)$$	SVD or MF stability under perturbation (Valderrama et al., 2024)
Solar-wind analog ensembles	Spectral-ratio diagnostics $(a,b)$ and predictability surface $P(\tau,f)$	Frequency-domain fidelity of forecasts (Simon et al., 18 Apr 2025)
Markovian communication networks	$D_n(L)$ with spectral upper bounds	TV predictability controlled by eigenvalues (Mostafavi et al., 2024)

A plausible implication is that “spectral” is used in at least four non-equivalent senses: Fourier spectra, multifractal singularity spectra, singular-value spectra, and Markov-chain eigenspectra. The shared idea is not the representation itself but the attempt to map structural regularity into an ex ante statement about forecastability.

2. Entropy-rescaled spectral concentration for univariate time series

In the time-series formulation of forecastability, the spectral predictability score is a model-agnostic, frequency-domain measure for a de-trended univariate series $y_0,\dots,y_{T-1}$. One computes the power spectral density via the FFT, normalizes the powers into a pmf

$\Delta\alpha$0

defines spectral entropy

$\Delta\alpha$1

and rescales it to

$\Delta\alpha$2

Low entropy implies that energy is concentrated in a small number of frequencies, whereas high entropy corresponds to a flat, noise-like spectrum. The paper interprets values near $\Delta\alpha$3 as highly predictable and values near $\Delta\alpha$4 as highly complex or unpredictable (Wang et al., 17 Jul 2025).

The computation pipeline is explicit: detrend or remove mean/linear trend, apply a Hann window $\Delta\alpha$5 so that $\Delta\alpha$6, compute the one-sided PSD

$\Delta\alpha$7

normalize to obtain $\Delta\alpha$8, then evaluate $\Delta\alpha$9 and $$S_t=\omega_1\Delta\alpha_t+\omega_2\Delta f_t+\omega_3 B_t$$0. The stated complexity through the FFT stage is $$S_t=\omega_1\Delta\alpha_t+\omega_2\Delta f_t+\omega_3 B_t$$1, which makes the score practical for long series. The worked examples are deliberately extreme: a pure sine wave yields $$S_t=\omega_1\Delta\alpha_t+\omega_2\Delta f_t+\omega_3 B_t$$2 and $$S_t=\omega_1\Delta\alpha_t+\omega_2\Delta f_t+\omega_3 B_t$$3; white noise yields an approximately uniform spectrum and $$S_t=\omega_1\Delta\alpha_t+\omega_2\Delta f_t+\omega_3 B_t$$4; a noisy two-frequency signal can produce entropy large enough that normalization against $$S_t=\omega_1\Delta\alpha_t+\omega_2\Delta f_t+\omega_3 B_t$$5 gives a negative value, which is then truncated to $$S_t=\omega_1\Delta\alpha_t+\omega_2\Delta f_t+\omega_3 B_t$$6 in the illustrative calculation (Wang et al., 17 Jul 2025).

The paper also proposes score ranges for interpretation. $$S_t=\omega_1\Delta\alpha_t+\omega_2\Delta f_t+\omega_3 B_t$$7 near $$S_t=\omega_1\Delta\alpha_t+\omega_2\Delta f_t+\omega_3 B_t$$8 indicates strong, sharp periodicities; $$S_t=\omega_1\Delta\alpha_t+\omega_2\Delta f_t+\omega_3 B_t$$9 indicates moderate forecastability; $S=\sum_{k=1}^{K} w_k A(f_{(k)})$0 signals low forecastability. A practical guideline is to compare $S=\sum_{k=1}^{K} w_k A(f_{(k)})$1 to a matched white-noise baseline of the same length and sparsity. On the M5 competition data, using daily and weekly series across hierarchy levels and evaluating ETS, AutoGluon’s RecursiveTabular, and Chronos with WAPE, the reported relationship is a strong negative correlation of approximately $S=\sum_{k=1}^{K} w_k A(f_{(k)})$2 between $S=\sum_{k=1}^{K} w_k A(f_{(k)})$3 and forecasting error. The same study reports that $S=\sum_{k=1}^{K} w_k A(f_{(k)})$4 declines as one moves from more aggregated to more disaggregated hierarchy levels, and that aggregating daily data to weekly raises the product-level score from about $S=\sum_{k=1}^{K} w_k A(f_{(k)})$5 to about $S=\sum_{k=1}^{K} w_k A(f_{(k)})$6 while reducing error (Wang et al., 17 Jul 2025).

Several caveats are explicit. Detrending and window choice materially affect the estimate; a Hann window is recommended to reduce leakage. The score stabilizes for $S=\sum_{k=1}^{K} w_k A(f_{(k)})$7. Moderate sparsity, up to roughly $S=\sum_{k=1}^{K} w_k A(f_{(k)})$8–$S=\sum_{k=1}^{K} w_k A(f_{(k)})$9, inflates $$\mathrm{SPS}(\epsilon)= (\lambda/f_0)[\ln(1/\epsilon)]^{1/\beta}$$0 slightly, whereas extreme sparsity above $$\mathrm{SPS}(\epsilon)= (\lambda/f_0)[\ln(1/\epsilon)]^{1/\beta}$$1 can distort the spectrum. Rolling-window computation is suggested for non-stationarity and regime shifts. The paper also states that $$\mathrm{SPS}(\epsilon)= (\lambda/f_0)[\ln(1/\epsilon)]^{1/\beta}$$2 cannot distinguish deterministic chaos from purely random noise, which motivates pairing it with a largest-Lyapunov-exponent analysis when that distinction matters (Wang et al., 17 Jul 2025).

3. Multifractal and harmonic constructions in financial series

In high-frequency equity-index data, MF-DFA provides a different route from raw returns to a spectral predictability quantity. For one-minute log-returns $$\mathrm{SPS}(\epsilon)= (\lambda/f_0)[\ln(1/\epsilon)]^{1/\beta}$$3 in a moving window of length $$\mathrm{SPS}(\epsilon)= (\lambda/f_0)[\ln(1/\epsilon)]^{1/\beta}$$4, one constructs the cumulative profile

$$\mathrm{SPS}(\epsilon)= (\lambda/f_0)[\ln(1/\epsilon)]^{1/\beta}$$5

splits it into segments of size $$\mathrm{SPS}(\epsilon)= (\lambda/f_0)[\ln(1/\epsilon)]^{1/\beta}$$6, removes local polynomial trends $$\mathrm{SPS}(\epsilon)= (\lambda/f_0)[\ln(1/\epsilon)]^{1/\beta}$$7, computes segment-wise detrended variances

$$\mathrm{SPS}(\epsilon)= (\lambda/f_0)[\ln(1/\epsilon)]^{1/\beta}$$8

and then defines the $$\mathrm{SPS}(\epsilon)= (\lambda/f_0)[\ln(1/\epsilon)]^{1/\beta}$$9th-order fluctuation function $$\mathrm{SPS}=1-\mathrm{RMSE}_{\mathrm{SPS}}/(\max-\min)$$0. Multifractality is expressed through

$$\mathrm{SPS}=1-\mathrm{RMSE}_{\mathrm{SPS}}/(\max-\min)$$1

from which one obtains

$$\mathrm{SPS}=1-\mathrm{RMSE}_{\mathrm{SPS}}/(\max-\min)$$2

The width of the multifractal spectrum,

$$\mathrm{SPS}=1-\mathrm{RMSE}_{\mathrm{SPS}}/(\max-\min)$$3

is treated as a scalar measure of multifractality, with larger $$\mathrm{SPS}=1-\mathrm{RMSE}_{\mathrm{SPS}}/(\max-\min)$$4 indicating stronger intermittency or volatility clustering (Fu et al., 2018).

That scalar is then embedded in predictive regressions for excess returns:

$$\mathrm{SPS}=1-\mathrm{RMSE}_{\mathrm{SPS}}/(\max-\min)$$5

or, with multiple spectrum-derived features,

$$\mathrm{SPS}=1-\mathrm{RMSE}_{\mathrm{SPS}}/(\max-\min)$$6

where $$\mathrm{SPS}=1-\mathrm{RMSE}_{\mathrm{SPS}}/(\max-\min)$$7. Estimation is by OLS with Newey–West standard errors. Out-of-sample performance is summarized by

$$\mathrm{SPS}=1-\mathrm{RMSE}_{\mathrm{SPS}}/(\max-\min)$$8

with significance assessed by the Clark–West adjusted-MSFE test. In the summary provided, one may further define

$$\mathrm{SPS}=1-\mathrm{RMSE}_{\mathrm{SPS}}/(\max-\min)$$9

with weights taken from in-sample OLS coefficients, and call $(a,b)$0 the spectral predictability score. The stated conclusion is that $(a,b)$1 is a significant and positive excess-return predictor, and that the combined score can deliver stronger out-of-sample performance than any single component alone (Fu et al., 2018).

A separate harmonic-analysis line of work builds a score directly from dominant Fourier components of detrended monthly stock-value indices. The preprocessing pipeline includes deflation by CPI, optional removal of exogenous-shock windows, polynomial trend removal by OLS, and optional stationarity checks. Once the residual series $(a,b)$2 is treated as stationary, the DFT

$(a,b)$3

or its real trigonometric form is computed, typically via FFT, with Welch’s method and a Hanning window used to suppress leakage; Lomb–Scargle is suggested for irregularly sampled data. The periodogram is

$(a,b)$4

and Parseval’s theorem gives

$(a,b)$5

The score is then formed by ranking frequencies by descending power, selecting the top $(a,b)$6, and taking

$(a,b)$7

In the cited implementation, equal weights are used for the first five harmonics, so $(a,b)$8. The justification for $(a,b)$9 is empirical: the periodogram plots indicate that five peaks explain a very large share of total variance, typically $P(\tau,f)$0–$P(\tau,f)$1, and the resulting five-harmonic reconstruction was sufficient to anticipate the late-2008 downturn in the US, German, and Japanese markets in a near-out-of-sample test cut at July 2008 (Romana et al., 2023).

These two financial usages are technically distinct. One encodes predictability in the geometry of a multifractal singularity spectrum; the other encodes it in the aggregate amplitude of a few dominant harmonics. This suggests that, within finance, “spectral predictability score” is better understood as a family resemblance among summary statistics derived from scale- or frequency-domain structure than as a single reproducible formula.

4. Spectral decay, Lyapunov scales, and smooth versus rough predictability

In chaotic dynamical systems and climate dynamics, predictability is linked to the asymptotic form of the power spectrum. The cited work recalls Lorenz’s intrinsic-horizon relation

$P(\tau,f)$2

where $P(\tau,f)$3 is the maximal Lyapunov exponent and $P(\tau,f)$4 is the initial error. It then distinguishes smooth from rough predictability through the high-frequency decay of the spectrum:

$P(\tau,f)$5

The climate examples reported in the summary show stretched-exponential spectra for leading large-scale indices such as AO, NAO, PNA, ISM, and Niño 3.4, with Hamiltonian-motivated exponents $P(\tau,f)$6 or $P(\tau,f)$7. By contrast, the unsmoothed Madden–Julian Oscillation indices exhibit $P(\tau,f)$8, which is interpreted as rough predictability; after applying a 3-day running mean, the MJO spectrum becomes stretched exponential again with $P(\tau,f)$9 (Bershadskii, 2018).

The summary then introduces a synthesized spectral predictability score by combining the spectral cut-off $D_n(L)$0, the associated timescale $D_n(L)$1, the Lyapunov scale $D_n(L)$2, and the initial error $D_n(L)$3. The proposed score is

$D_n(L)$4

Its interpretation is explicit. Larger $D_n(L)$5 raises predictability; larger $D_n(L)$6 lowers it; smaller $D_n(L)$7 amplifies the gain from reducing $D_n(L)$8. In the limit $D_n(L)$9, corresponding to power-law rough spectra, the formula breaks down, which the summary interprets as signaling that the horizon cannot be pushed arbitrarily far by shrinking initial error (Bershadskii, 2018).

Illustrative calculations are provided. For the Arctic Oscillation, using $y_0,\dots,y_{T-1}$0, $y_0,\dots,y_{T-1}$1, $y_0,\dots,y_{T-1}$2, $y_0,\dots,y_{T-1}$3, and $y_0,\dots,y_{T-1}$4, the score is approximately $y_0,\dots,y_{T-1}$5. For the smoothed MJO, with $y_0,\dots,y_{T-1}$6, $y_0,\dots,y_{T-1}$7, $y_0,\dots,y_{T-1}$8, $y_0,\dots,y_{T-1}$9, and the same $\Delta\alpha$00, the score is approximately $\Delta\alpha$01. The same spectral logic is also extended in the summary to ensemble-weather-forecast error fields in spatial wavenumber, where approximately exponential spectra suggest a corresponding spatial analogue of the score (Bershadskii, 2018).

This formulation differs from the entropy-based and multifractal variants in one decisive respect: it is explicitly horizon-oriented. Rather than assigning a generic “predictability” value to a series, it links a spectral tail law to the extent by which a reliable forecast horizon can exceed one Lyapunov time for a chosen error tolerance.

5. Singular-value and matrix-factorization stability in recommender systems

In recommender systems, the spectral predictability score is defined on the user–item rating matrix rather than on a univariate time series. Let $\Delta\alpha$02 be the rating matrix with unknown entries set to $\Delta\alpha$03, and let $\Delta\alpha$04 be the set of observed ratings. A perturbation fraction $\Delta\alpha$05 is fixed, a subset $\Delta\alpha$06 of size $\Delta\alpha$07 is chosen uniformly at random, and the ratings on those positions are permuted to obtain a perturbed matrix $\Delta\alpha$08. With

$\Delta\alpha$09

a structural reconstruction is formed as

$\Delta\alpha$10

where $\Delta\alpha$11 approximates the singular-value correction induced by restoring the true entries. The unnormalized predictability measure is

$\Delta\alpha$12

and a normalized score may be reported as

$\Delta\alpha$13

High SPS corresponds to low perturbation-reconstruction error and thus to stronger intrinsic predictability (Valderrama et al., 2024).

The SVD-based approximation is made explicit through

$\Delta\alpha$14

followed by projection into the singular-vector basis:

$\Delta\alpha$15

Coordinate-wise,

$\Delta\alpha$16

The same paper also defines an MF-based variant, ESC, in which a $\Delta\alpha$17-dimensional matrix factorization is fit to $\Delta\alpha$18, the masked entries are predicted directly, and the procedure is repeated several times and averaged. The underlying assumption is that well-structured low-rank data should be spectrally stable under small random perturbations (Valderrama et al., 2024).

The empirical study covers 12 real-world datasets, each sampled to 100K ratings, from Amazon categories, MovieLens 100K, Netflix Prize subsets, and Steam reviews. The collaborative-filtering baselines are NMF (20 dims), biased-TSVD (20 dims), SVD++, KNN ($\Delta\alpha$19), KNNMeans ($\Delta\alpha$20), SlopeOne, and Co-clustering, with a 50/50 train/test split and normalized RMSE as the accuracy metric. Correlations between SPS and the best algorithm’s test RMSE are reported as follows: ASC (the SVD-based version) achieves Pearson $\Delta\alpha$21 and Spearman $\Delta\alpha$22, while ESC achieves Pearson $\Delta\alpha$23 and Spearman $\Delta\alpha$24. On synthetic matrices with controlled structure and $\Delta\alpha$25 sparsity, ASC fails to distinguish some regimes, with Pearson approximately $\Delta\alpha$26, whereas ESC remains strongly correlated at approximately $\Delta\alpha$27. The practical recommendations are $\Delta\alpha$28–$\Delta\alpha$29 and, for ESC, about $\Delta\alpha$30 latent factors with about $\Delta\alpha$31–$\Delta\alpha$32 repetitions (Valderrama et al., 2024).

Compared with the time-series formulations, this version broadens the meaning of “spectral” from Fourier concentration to latent-space stability. The score is still model-agnostic in intent, but the structure being probed is the singular spectrum of a partially observed matrix.

6. Frequency-domain diagnostics for Analog Ensemble solar-wind forecasts

In Analog Ensemble forecasting of solar-wind parameters, the spectral dimension of predictability is defined through the fidelity of forecast spectra relative to observed spectra. Let $\Delta\alpha$33 be the target quantity, $\Delta\alpha$34 for $\Delta\alpha$35 the reference pattern, and $\Delta\alpha$36 candidate historical blocks. Analog selection is based on the mean squared distance

$\Delta\alpha$37

with the first $\Delta\alpha$38 ranked blocks forming the ensemble. Each analog continues into an individual forecast $\Delta\alpha$39 for $\Delta\alpha$40, and the usual reduced forecast is the pointwise mean

$\Delta\alpha$41

Time-domain performance is measured by RMSE, NRMSE, and skill relative to persistence, climatology, or synodic recurrence baselines (Simon et al., 18 Apr 2025).

The spectral metric is the spectral ratio

$\Delta\alpha$42

where $\Delta\alpha$43 and $\Delta\alpha$44. For frequencies above a threshold, typically $\Delta\alpha$45, the paper fits

$\Delta\alpha$46

Here $\Delta\alpha$47 is the slope of the small-scale bias and $\Delta\alpha$48 is the spectral ratio at $\Delta\alpha$49. Small $\Delta\alpha$50 indicates limited divergence of spectral slopes, while $\Delta\alpha$51 indicates little net power mismatch near $\Delta\alpha$52. These parameters function as summary diagnostics of spectral predictability (Simon et al., 18 Apr 2025).

Because mean reduction suppresses small-scale power through phase cancellation, the paper introduces a spectral reduction algorithm. For each individual forecast one computes the amplitude spectrum $\Delta\alpha$53, then forms the geometric-mean amplitude spectrum

$\Delta\alpha$54

combines it with the phase of the mean-reduced forecast, $\Delta\alpha$55, constructs

$\Delta\alpha$56

and inverts the transform to obtain $\Delta\alpha$57. By construction, the reduced series preserves the ensemble’s geometric-mean amplitude spectrum while retaining the mean forecast’s large-scale phase (Simon et al., 18 Apr 2025).

The reported case study uses a proton-speed forecast launched on 6 Oct 2004 14:58 UTC, with $\Delta\alpha$58, $\Delta\alpha$59, and forecast sizes of 1 day and 42 days. At 1 day, NRMSE is $\Delta\alpha$60 for $\Delta\alpha$61 and $\Delta\alpha$62 for $\Delta\alpha$63, compared with $\Delta\alpha$64 for persistence. The spectral-ratio fit over $\Delta\alpha$65–$\Delta\alpha$66 gives $\Delta\alpha$67, $\Delta\alpha$68 for $\Delta\alpha$69 and $\Delta\alpha$70, $\Delta\alpha$71 for $\Delta\alpha$72. At 42 days, the mean-reduced forecast has $\Delta\alpha$73, $\Delta\alpha$74, while the spectral-reduced forecast has $\Delta\alpha$75, $\Delta\alpha$76. Predictability in the time domain is defined as the fraction of reference intervals for which skill is positive, with reported values of $\Delta\alpha$77 for $\Delta\alpha$78 and $\Delta\alpha$79 for $\Delta\alpha$80 for proton speed, and optimal leads of $\Delta\alpha$81 and $\Delta\alpha$82, respectively (Simon et al., 18 Apr 2025).

This usage differs from scalar pre-training scores. Here spectral predictability is a lead-time- and frequency-dependent diagnostic of how well a forecast preserves multiscale variance, and the proposed score is closer to a performance surface than to a single number.

7. Markov-chain eigenspectra, total variation, and cross-domain interpretation

In communication networks under Markovian dynamics, predictability is defined in probabilistic rather than Fourier terms. Let $\Delta\alpha$83 be the performance metric $\Delta\alpha$84 slots ahead, with forecast distribution

$\Delta\alpha$85

and marginal distribution

$\Delta\alpha$86

Predictability at lead time $\Delta\alpha$87 is the total-variation distance

$\Delta\alpha$88

An $\Delta\alpha$89-predictable horizon is then

$\Delta\alpha$90

The underlying conditions are modeled as a finite, reversible, irreducible, aperiodic Markov chain with eigenvalues $\Delta\alpha$91, second-largest magnitude eigenvalue

$\Delta\alpha$92

and spectral gap $\Delta\alpha$93. The paper derives the bound

$\Delta\alpha$94

and the simpler form

$\Delta\alpha$95

where

$\Delta\alpha$96

Here $\Delta\alpha$97 is the condition-specific posterior kernel (Mostafavi et al., 2024).

For a Geo/Geo/1/K queue, the queue-length process has eigenvalues

$\Delta\alpha$98

with $\Delta\alpha$99. The stationary queue-length law satisfies $$S_t=\omega_1\Delta\alpha_t+\omega_2\Delta f_t+\omega_3 B_t$$00, with $$S_t=\omega_1\Delta\alpha_t+\omega_2\Delta f_t+\omega_3 B_t$$01, and the delay posterior at state $$S_t=\omega_1\Delta\alpha_t+\omega_2\Delta f_t+\omega_3 B_t$$02 is $$S_t=\omega_1\Delta\alpha_t+\omega_2\Delta f_t+\omega_3 B_t$$03. The exact predictability formula is obtained by substituting the transient and stationary probabilities into the TV expression, and a large-$$S_t=\omega_1\Delta\alpha_t+\omega_2\Delta f_t+\omega_3 B_t$$04 approximation is also reported. For multi-hop tandem queues, total variation is subadditive under convolution, giving

$$S_t=\omega_1\Delta\alpha_t+\omega_2\Delta f_t+\omega_3 B_t$$05

and hence a hopwise spectral bound obtained by summing the per-hop contributions (Mostafavi et al., 2024).

The design implications are direct: a small spectral gap means slow mixing and hence longer predictability; rare states, reflected in large $$S_t=\omega_1\Delta\alpha_t+\omega_2\Delta f_t+\omega_3 B_t$$06, produce higher instantaneous predictability; and larger posterior-separation factor $$S_t=\omega_1\Delta\alpha_t+\omega_2\Delta f_t+\omega_3 B_t$$07 strengthens the bound. The paper also gives a sampling criterion for maintaining $$S_t=\omega_1\Delta\alpha_t+\omega_2\Delta f_t+\omega_3 B_t$$08-level forecast fidelity:

$$S_t=\omega_1\Delta\alpha_t+\omega_2\Delta f_t+\omega_3 B_t$$09

This formulation is the furthest from the Fourier-entropy notion, yet it preserves the same logic: predictability depends on how quickly the system’s spectral modes erase information about the present (Mostafavi et al., 2024).

Taken together, these literatures suggest a stable cross-domain template. A spectral predictability score first chooses a representation in which regularity is measurable, then compresses that regularity into a scalar or low-dimensional statistic, and finally interprets stronger concentration, wider or more informative scaling structure, greater stability under perturbation, flatter forecast-vs-truth spectral mismatch, or slower modal decay as evidence of longer or more reliable predictability. The principal misconception is therefore to treat the term as denoting one formula. In the cited literature, it denotes several non-equivalent constructions whose shared purpose is to quantify inherent predictive structure before or alongside downstream forecasting.