SSM-Audit – Finance Defaults and Worked Examples (0E.4–0E.7)

0E.4 — Forecast vs Actuals stability

Classical KPI (unchanged). Use the actual you already track (for example, daily revenue):

m := actual

Lane (residual stability).

r := actual - forecast
a_resid := tanh( k*( 1 - |r|/s ) )   # s > 0 is a scale (e.g., rolling MAD), k > 0 is sensitivity

Optional volatility add-on (visual entropy). Track calm vs churn with a decaying history, then map to a lane.

Entropy_t := log( Var(x_{0:t}) + 1 ) * exp( -lambda*t )    # t is lookback index or day count
a_vol := tanh( c*( 1 - Entropy_t / E0 ) )                  # E0 > 0 baseline

Blend residual and volatility in rapidity (order-invariant).

a := tanh( ( alpha*atanh(a_resid) + (1 - alpha)*atanh(a_vol) ) / max( alpha + (1 - alpha), 1e-12 ) )
# default alpha = 0.7

Clamp + parity (always).

a := clamp(a, -1+eps_a, +1-eps_a)
phi((m,a)) = m

Worked example (residual only).

forecast = 1_000_000
actual   =   980_000
r = -20_000
s = 50_000
k = 1.2

1 - |r|/s = 1 - 0.4 = 0.6
k*(...)   = 1.2*0.6 = 0.72
a_resid   = tanh(0.72) ≈ 0.617   -> band A+

If the same miss repeats, the lane trends downward even when the month still “hits plan”, prompting a “fix noise” action.

0E.5 — Tuning guide (pick once, document in manifest)

  • AR coverage window. Declare the policy (for example, <= 30 days). Keep the window stable; let the lane move, not the rule.
  • Refunds bound b. Set near acceptable daily reconciliation noise (for example, b = 0.005 for 0.5 percent). Backfill a calm month to sanity-check.
  • Forecast scale s. Prefer a robust scale (rolling MAD) in heavy-tail series; start k in [1.0, 1.5].
  • Volatility half-life. lambda := ln(2)/T_half. Default T_half = 14 days for executive rhythm; shorten for faster lines.

Pin these choices in the manifest so knobs_hash is meaningful and replays are exact.

0E.6 — Dashboarding pattern (practical)

  • Keep the existing m line or table unchanged.
  • Add a small badge or underlay for a with the band (A++/A+/A0/A-/A--).
  • Slice by segment/region/age weekly; stability debt hides in blends.
  • Executive view shows band counts; owner view shows a trends and the stamped CSV link.

0E.7 — Acceptance (module-specific)

  • AR: parity on m; visible a_cov drift when within-window coverage weakens; at least one tail action taken earlier than before.
  • Refunds: parity on m; sustained a_agree decline triggers a reconciliation deep-dive before month-end.
  • Forecasts: parity on m; repeated small residuals or rising volatility trigger plan or ops fixes within the pilot window.

Navigation
Previous: SSM-Audit – Finance Defaults and Worked Examples (0E.1–0E.3)
Next: SSM-Audit – Standards and Disclosure Positioning (0F)

Directory of Pages
SSM-Audit – Table of Contents

Frequently asked questions
SSM-Audit – Q & A