Regime-Switching Bootstrap

The critique is Lopez de Prado's and it is hard to argue with: a single covariance matrix estimated over two decades cannot encode the fact that the econometric relationship between assets changes. The 2008 correlation structure is not the 2017 correlation structure, and averaging them produces a matrix that describes neither.

The regime process does not estimate a global covariance matrix at all. Returns are drawn from regime-labeled historical rows, and the chain carries the dynamics: persistence, crisis clustering, and conditioning on where the market is today. Those are exactly the features a static cannot represent.

Compared with the plain block bootstrap, which treats every historical day as equally likely to be tomorrow, this adds two things: multi-month persistence of stressed conditions, and the ability to start the simulation in a chosen state.

A Hamilton (1989) Markov-switching model with switching variance is fitted to the portfolio-level daily return series, using the same estimation machinery that already backs the HMM Regime MVO optimization method in production. The latent state follows a first-order Markov chain,

with either 2 or 3. The fit hands the sampler four things:

• Per-day regime labels from filtered probabilities. The filtering recursion at day uses observations only through day , though the parameters themselves are estimated on the full calibration sample. This is retrospective calibration, not an out-of-sample fit, and the docs say so rather than implying a live forecast.
• The transition matrix , oriented row-stochastic, whose diagonal controls how long each state persists. The implied mean duration of state is .
• Two start distributions: the filtered probabilities at the last observation, which is “today's regime” and the default, and the chain's stationary distribution.
• The bear state, identified as the highest-variance regime. Identifying by a fitted moment rather than by label sidesteps the EM label-switching ambiguity entirely.

The fit is deterministic given the data. The optimizer runs from the library default start plus a fixed set of seeded perturbed starts, and the best-likelihood converged candidate wins, so reproducibility from the echoed configuration is preserved.

Each path carries a latent regime advanced daily by . While the state holds, sampling advances along true calendar order inside one contiguous historical episode of that regime, with geometric block restarts as in the plain bootstrap. A block ends when any of three things happens:

• the Markov chain switches state;
• a geometric restart fires;
• the current contiguous episode of that regime ends in history.

The third condition is what keeps the process honest. Without it, a path could step from the last day of one bear episode straight to the first day of a different bear episode years later and emit them as adjacent observations. Because continuation stops at episode boundaries, two nonconsecutive historical days are never presented as consecutive. Regime persistence is carried by the Markov chain, not by splicing unrelated rows together.

As with the plain bootstrap, whole rows are sampled, so cross-asset correlation, skew and kurtosis are preserved exactly, and the sampled global row indices are reported so calendar-aligned CPI reuse still works.

A regime model that has not actually found regimes is worse than no regime model, because it dresses estimation noise as structure. Six checks must pass, and the run needs at least 252 observations to attempt the fit at all. If any check fails, the engine falls back to the plain stationary bootstrap and reports the reason in the result's regime block. It never fails silently and it never presents a rejected fit as if it had succeeded.