# Fixed evaluation specification

Recorded before any held-out errors were computed, 2026-09-24.

Source: NOAA GML https://gml.noaa.gov/webdata/ccgg/trends/co2/co2_mm_mlo.txt (snapshot created 2026-09-05; MD5 35591deeaf110bca96cc64a7ec337994). Analyze monthly average (ppm), not the published deseasonalized series, March 1958–December 2025. Retain the original file including later rows but never use 2026 values in calculations.

NOAA flags interpolated months with negative standard deviation and uncertainty; apply that flag only from May 1974 onward, because earlier Scripps values have unavailable quality metadata encoded negatively. Retain early Scripps values, acknowledging unidentified interpolation. Treat negative monthly averages as missing. Preserve the regular monthly grid; no additional imputation. Retain documented Maunakea substitutions (December 2022–July 4, 2023).

Expanding training window starts March 1958 and ends at origin t. Monthly origins December 2020–November 2025. Refit SARIMA (0,1,1)(0,1,1)[12] at each origin, via base R stats::arima(method='ML', include.mean=FALSE), with state-space missing-observation handling and default optimizer, no tuning or deterministic trend. Forecast horizons h=1,6,12 months. Score only observed, nonflagged targets January 2021–December 2025; report fitting failures and common eligible sample counts.

Seasonal naive: y[t+h-12]. Seasonal drift: y[t+h-12] + mean(y[i]-y[i-12]) for valid pairs with i in t-59,...,t. Drift requires at least 12 valid pairs and both baselines require the seasonal lag. All inputs must be available by t. Compare MAE, RMSE and signed prediction-minus-observation bias on targets shared by all models. Also retain per-model eligibility.

SARIMA central 80% and 95% prediction intervals: predicted mean +/- qnorm(.90 or .975) times forecast standard error. Report empirical coverage and mean widths by horizon; these intervals condition on fitted parameters and Gaussian errors. Diagnose convergence and residual dependence without test-driven modification. Overlapping forecasts are dependent; do not interpret nominal binomial confidence intervals or independent-error tests as valid.

Descriptions use complete-year annual means and within-decade linear detrending for monthly seasonal profiles. No full-record transformations enter forecasting. Evaluation is a current-vintage historical simulation, not a real-time vintage backtest. No future forecast beyond 2025 is needed.