Summary

Given the state variables defined in Regime Definition, a system still has to choose how labels are produced: hand-set rules, statistical state models (HMMs), or change-point detection. The decisive comparison is not in-sample accuracy but detection latency and ex-ante validity — every method confirms a new regime only after it has begun, and the label must be generated from data available at the time the label is used¹. This concept catalogues the three families honestly, including how long each typically takes to flip a label.

Rule-Based Bands

Hand-set thresholds on the state variables (VIX band, term slope, VRP sign) with confirmation rules and hysteresis.

• How: fixed bands or rolling-percentile bands on prior-close data; enter at threshold X, exit at threshold X±buffer; require N consecutive days.
• Latency: typically 1–5 trading days for a real regime shift (confirmation lag is a deliberate price paid for stability against flicker). Fast breakouts (Volmageddon-class) can flip the label in 1 day if the confirmation rule is permissive, but permissive rules also mislabel spikes that mean-revert within days.
• Strengths: transparent, trivially point-in-time auditable, no fit to overfit, no lookahead, cheap. Every book-derived condition ("calm", "typhoon")⁵ maps directly onto a band.
• Weaknesses: bands are static; multivariate interactions (high VIX but steep contango) require manual case rules; thresholds are judgment, so document them.

Hidden Markov Models

Fit a small (2–4 state) HMM to returns and/or vol features; the regime is the filtered most-likely state¹.

• How: features = daily index returns, realized vol, VIX level and slope. Fit by EM on trailing data; at decision time use the filtered probability P(stateₜ | data ≤ t) — never the smoothed probability P(stateₜ | full sample), which is lookahead.
• Latency: an HMM's filtered state probability reacts within ~1–3 days to a sharp shift, but EM fits on trailing windows mean the model itself is refit with lag; a state discovered in-sample may not exist in the refit until weeks later. Persistent low-vol/high-vol states detect reliably; short V-shaped events are mostly missed until after they resolve.
• Strengths: probabilistic output (use P>0.7 gates rather than hard labels), captures correlation shifts, principled multivariate treatment.
• Weaknesses: label switching across refits (state 1 vs state 2 are arbitrary), fit instability, and the classic trap: in-sample decoded regimes look beautifully separated and are worthless as a trading signal.

Change-Point Detection

CUSUM and Bayesian Online Changepoint Detection (BOCPD) flag when the data-generating process shifted, rather than classifying states³².

• How: CUSUM accumulates deviations from a running baseline and alarms when the cumulative statistic crosses a design threshold (tuned via average run length). BOCPD maintains a run-length posterior, online, one observation at a time.
• Latency: CUSUM's latency is a tunable tradeoff — the faster the detection, the higher the false-alarm rate; expect several days of accumulation for vol-regime shifts that build over days, near-immediate response to jumps. BOCPD reacts in ~1–2 days to clear level shifts with an explicit probability of change.
• Strengths: honest about the transition moment; the transition signal itself is the output — which maps directly to the "no new risk during transitions" rule in Regime-Dependent Delta Exposure.
• Weaknesses: detection only, not classification (you still need bands or an HMM to say which regime); CUSUM threshold tuning is subtle.

Comparison

Method	Typical detection delay	Lookahead traps	Output	Practical role
Rule bands	1–5 days (confirmation)	Rolling percentiles must trail; fixed bands safe	Hard label	Default; VIX-band × slope × VRP set
HMM (filtered)	~1–3 days for persistent shifts; misses V-shapes	Smoothed probabilities; refit on full history	Posterior per state	Cross-check on bands; P>0.7 gate
CUSUM / BOCPD	0–2 days for jumps; days for drifts	Backtest alarms must use only past data	Change event + probability	Transition trigger / risk-off switch

In-Sample Fit vs Ex-Ante Usefulness

A high in-sample regime-classification accuracy is not evidence of tradability. Two failure modes recur:

1. Smoothed/fitted labels: decoding the full series with the final fitted model gives every date a label that "knew" the future. Any backtest on those labels is lookahead.
2. Surviving-threshold tuning: bands chosen because they historically bracket the data will be silently re-tuned after every crash.

The honest metric is: run the detector as it would have run daily (filtered outputs only, refits on trailing windows), then measure (a) detection delay per true regime change, (b) false-flip rate per year, (c) downstream P&L of the regime-gated rules vs the ungated baseline, net of costs per the EV contract.

Validation Approach

• Point-in-time replay: regenerate all labels daily from data ≤ decision time; store labels, don't post-hoc classify.
• Walk-forward: refit (HMM/CUSUM thresholds) on trailing windows only; freeze and log every refit for auditability, in the spirit of TOMIC's operational infrastructure⁶.
• Regime-conditional baselines: per the EV contract, report VRP spread and a GARCH/HAR vol forecast ⁴ as the baseline within each regime; a regime rule earns its keep only if it beats the ungated baseline net of costs.
• Stress the labels: perturb thresholds/parameters ±20% and check the downstream conclusion survives; if the edge exists only at one threshold value, it does not exist.
• Delay accounting: for each historical regime change, record when each method actually flipped; publish the distribution, not the best case.

Links

• Regime Definition — the state variables these methods consume
• Regime-Dependent Delta Exposure — what the labels are used for
• Vol Forecasting Baselines — VRP inputs and forecast discipline
• Value at Risk (Hull) — EWMA/GARCH vol estimation background

References

• Hamilton, J. (1989). "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle." Econometrica 57(2), 357–384. https://doi.org/10.2307/2938279
• Adams, R. & MacKay, D. (2007). "Bayesian Online Changepoint Detection." arXiv:0710.3742. https://arxiv.org/abs/0710.3742
• Page, E. S. (1954). "Continuous Inspection Schemes." Biometrika 41(1–2), 100–115. https://doi.org/10.1093/biomet/41.1-2.100
• Nystrup, P. et al. (2015). "Regime-based versus static asset allocation: Letting the data speak." Journal of Asset Management 16 — HMM filtering vs in-sample decoding pitfalls. https://doi.org/10.1057/jam.2015.19

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1. Hamilton's regime-switching framework; the filtered (not smoothed) probability is the only ex-ante quantity. ↩↩

2. BOCPD gives online, causal run-length posteriors — detection delay is explicit and tunable. ↩

3. CUSUM: latency vs false-alarm tradeoff set by the decision threshold via average run length. ↩

4. EWMA/GARCH vol estimation as the forecast baseline in Hull VaR. ↩

5. The books' qualitative condition language formalized by band rules in Natenberg volatility. ↩

6. Auditability and operational discipline of a rules-based desk in TOMIC infrastructure. ↩