1. How long does a market regime last?
A regime lasts as long as the declared classification rule remains in the same state on its declared clock. There is no universal duration independent of those choices. A monthly growth classification and a session-level volatility classification produce different spells even over identical calendar coverage. Define a spell as consecutive eligible observations carrying the same label, and state whether length counts occupied observations or elapsed time between timestamps. Also specify what ends it: an observed different state, an abstention, a missing release, or the end of available coverage. These are measurement choices, not evidence that one definition tracks a true hidden cycle.
2. Do not turn the sample edge into an observed exit
An unfinished spell at the archive's right edge is right-censored: it has survived through the observed interval, but its eventual end is unknown. A state already active at the first observation has an unknown start and cannot simply be treated as a newly initiated complete spell. Keep these two boundary problems separate. Statsmodels' duration documentation explains right-censoring and methods designed to retain such information. Its examples are not regime studies, and using the vocabulary does not establish that a market-state sample satisfies a survival model's assumptions. A complete-spell average should disclose which boundary observations it excludes and why.
3. Inspect a constructed spell ledger
Consider three invented A spells observed from their starts on a regular decision clock. The first exits after two occupied periods, the second after four, and the third remains A through five periods when the archive ends. The complete-spell mean is therefore three periods, using only the first two. Averaging the three visible lengths gives eleven divided by three, or 3.6667 periods, but incorrectly treats the unfinished spell as an observed five-period duration. The table preserves the exit indicator instead. Neither number estimates a real market's persistence, and the censored spell could ultimately be much longer than its visible portion.
4. Understand what a survival curve retains
A survival description asks what fraction of spells remain active beyond a specified age. In the fictional ledger, a product-limit calculation starts with three spells at risk: the exit at age two leaves survival two-thirds, and the exit at age four leaves one-third. Censoring at age five removes the remaining observation without asserting a new exit. This construction illustrates accounting for incomplete follow-up; it does not establish a reliable curve from three spells. Independence, comparability across start dates and the mechanism ending follow-up require scrutiny. Uncertainty near the tail is particularly important when only one spell remains under observation.
5. Expected Markov duration answers a different question
Under a homogeneous first-order Markov model, self-transition probability p implies a geometric duration with mean one divided by one minus p, counting the initial occupied period. That is a property of the assumed transition process, not a direct average of a particular archive. Observed exit frequency can depend on spell age, previous states, release timing or a confirmation rule, violating the simple memoryless description. MIT's finite-state Markov notes supply the model framework; they do not certify a particular classification. Compare empirical spell records with model-implied duration only after aligning clocks and explicitly documenting those additional assumptions in the research specification.
6. Missingness and revisions can manufacture persistence
Carrying a monthly feature onto daily rows can create many repeated labels without new information. Likewise, treating unavailable rows as continuation quietly lengthens spells; treating them as exits quietly shortens spells. Keep a gap status and evaluate a separately declared bridging policy when useful. Revised data can also move a historical boundary, merge formerly separate spells or split one spell into several. Retain the contemporaneous and revised spell ledgers rather than presenting the latest reconstruction as an observation made at the time. Record whether each continuation follows a new release, a deliberate carry-forward or an unchanged input set repeated by the reporting calendar.
7. Questions that make a duration statement inspectable
Ask which event starts a spell, which event proves its end, and whether the last ongoing episode is visible in the denominator. Ask how many complete spells support the summary, how calendar exposure is distributed, and whether one long episode dominates occupancy. Check whether a claimed duration forecast was actually frozen before the future exit. Common failures include counting censored endpoints as exits, confusing occupied periods with elapsed intervals, and treating repeated stale labels as independent evidence. A useful publication reports complete lengths, incomplete follow-up, gap handling and the rule version together. It need not translate those descriptions into a trading instruction.
Inspect the comparison
| Synthetic A spell | Observed occupied periods | Exit observed | Complete-duration contribution |
|---|---|---|---|
| First | 2 | Yes | 2 |
| Second | 4 | Yes | 4 |
| Third | 5 | No: archive ends | Excluded, not an exit |
Primary references
References support the stated methods and data conventions. Original fictional examples are not observations from the cited sources.