This study develops a diagnostic analytics framework for evaluating whether an observed return process is compatible with a noise-driven conditional variance model within the GARCH family. Rather than proposing yet another GARCH extension for cryptocurrency markets, we adopt a null-universe perspective: if a market is adequately represented by a GARCH-type specification, the standardized innovations implied by the fitted model should resemble stable noise; if not, extreme standardized events should occur more often than predicted under the null. Using the S&P 500 index as a benchmark market across two eras (1962–1985 and 1986–2026), and Bitcoin at four time scales (30-minute, 1-hour, 4-hour, daily), we evaluate tail-event exceedances under both normal and Student-t innovations. This design treats the S&P 500 as an analytics calibration case and Bitcoin as an event-sensitive test environment for assessing whether model adequacy can be recovered through distributional refinement alone. We find that S&P 500 tail deviations are largely accommodated by moderate-tailed Student-t distributions (ν = 5.6–10.0), whereas Bitcoin exhibits substantially heavier standardized residual tails across frequencies. Estimated degrees of freedom for BTC (ν ≈ 3.0–4.0) approach the lower boundary of finite higher moments, and residual tail rejection persists at higher frequencies even under the Student-t specification. The results position the proposed null-universe test as a first-stage diagnostic checkpoint in analytics pipelines that depend on model-filtered residuals for downstream inference, risk scoring, or decision support — providing a structured basis for determining whether GARCH-type specifications offer adequate approximations before further analytical workflows are constructed upon them.