1. Identify the object being estimated
In a latent-state model, a state probability concerns membership in a model-defined hidden state. It is not automatically the probability of a recession, a positive return or a successful decision. Those interpretations require separately defined events and evidence. A deterministic threshold label is different: it follows a rule applied to features and does not become a probability by being displayed with confidence-like language. This guide explains probabilistic terminology for reading research. It does not imply that the synthetic two-feature threshold exercises train a hidden Markov model.
2. Distinguish the conditioning sets
For fixed model parameters, a predicted state probability at time t uses observations through t-1. A filtered probability incorporates the observation at t. A smoothed probability for t incorporates observations through a later sample endpoint T. Statsmodels' Markov autoregression example explicitly distinguishes filtering through t from smoothing over the full sample. Here t indexes model observations, not necessarily the wall-clock publication time of economic data. A monthly observation can enter the model only after its release, so a calendar label alone does not establish decision-time eligibility.
3. Check how the parameters became known
Filtering limits the observations used in the state-update calculation; it does not automatically limit the information used to estimate model parameters. If those parameters were fitted using the complete historical sample, an early filtered value still depends indirectly on later observations. The same issue applies to state-count selection, feature selection, scaling and initialisation choices. For a decision-time interpretation, document the training cutoff and all earlier selection stages. Either freeze a previously estimated specification or use a predeclared chronological refitting procedure. A filtered output field alone is insufficient evidence.
4. Keep revision look-ahead separate from smoothing
Replacing historical input values with later revisions changes the information set even if the algorithm only filters forward. Conversely, smoothing over first-release values still uses observations after the date being described. These are separate routes by which later information can enter an estimate. Record the vintage policy and probability type independently. If a result changes after an update, ask whether new observations, revised observations or refitted parameters caused the change. Calling every change 'smoothing' hides the distinction and makes the earlier decision impossible to assess fairly.
5. Follow a fictional observation timeline
Suppose three invented observations arrive on explicitly fictional dates 2030-04-10, 2030-04-11 and 2030-04-12. Assume the model parameters were frozen before the first arrival and no input revisions occur. For the middle observation, prediction uses the first arrival, filtering adds the middle arrival, and a retrospective smoother can also use the last arrival. The table records these information sets without inventing probability estimates. At the middle decision cutoff, the last observation is unavailable. Any retrospective inference using it belongs to a later analysis, even if plotted over the earlier date.
6. Read smoothness without awarding predictive credit
A smoother is useful for retrospective interpretation because later observations can inform an earlier hidden state. That does not make the reconstructed path a sequence of contemporaneous forecasts. Nor must smoothing increase confidence at every point: later evidence can challenge an earlier interpretation. Compare filtered and smoothed histories only with the parameter and input versions explicitly identified. Treat a change in the inferred turning point as a model revision to historical interpretation, not proof that an earlier decision process anticipated the turning point or could have acted on it.
7. Separate fitted evidence from external validation
A concentrated state probability is conditional on a specification, not evidence that the specification is correct. A fitted likelihood describes compatibility with the fitting data under model assumptions; it does not independently validate economic labels or future usefulness. Calibration needs a clearly observable evaluation target and suitable held-out observations. An unobserved latent regime does not supply its own ground-truth labels merely because the model names it. Report uncertainty about parameters, state meaning and measurement separately where the study can support it, rather than compressing everything into one confidence number.
8. Inspect the exact output before interpreting it
Statsmodels documents predicted, filtered and smoothed weighting options for MarkovRegression.predict, with smoothed as the documented default. A function called predict therefore needs inspection before its output is described as a historical forecast. Record the chosen output, parameter fit endpoint, data vintage, state mapping and intended decision cutoff. These checks are reading principles, not claims about software used by this publication. Without a fitted and independently evaluated experiment, no numerical state probabilities or predictive results are established here. This conceptual guide is not investment advice.
Inspect the comparison
| Estimate for fictional middle observation | Information admitted | Available at the middle cutoff? |
|---|---|---|
| Predicted state probability | Observations through fictional 2030-04-10 | Yes, under the frozen-parameter assumption |
| Filtered state probability | Observations through fictional 2030-04-11 | Yes, after that observation is validated |
| Retrospective smoothed state probability | Observations through fictional 2030-04-12 | No; the final observation arrives later |
Primary references
References support the stated methods and data conventions. Original fictional examples are not observations from the cited sources.