This paper shows that a simple, finite‑state hidden Markov model can reproduce three standard patterns in daily US equity returns — heavy tails (more extreme daily moves than a normal curve predicts), negligible average serial correlation (returns are hard to predict day‑to‑day), and volatility clustering (periods of large moves tend to cluster) — if each regime is allowed a heavy‑tailed distribution. Earlier work blamed ordinary Markov models for failing to match the slow decay of volatility clustering. The authors argue that the failure was not the Markov timing mechanism itself but the choice of per‑regime distributions.

The researchers use a continuous hidden Markov model (CHMM). In this model a small number of latent regimes (for example, “calm” and “volatile” market states) switch according to a Markov chain. Each regime emits daily returns from its own probability distribution (the emission). They fit four emission families under a single estimation framework: Gaussian (normal), Student‑t (heavier tails), Laplace (double‑exponential), and the Generalised Error Distribution (GED), which smoothly interpolates shapes between Laplace and Gaussian. Their estimation uses expectation‑maximization with shared forward‑backward recursions and a quantile‑based initialization that seeds each regime with a different slice of the return distribution.

To check whether limited Markov timing could still be a problem, they use a spectral identity that ties the number of distinct exponential decay modes in the absolute‑return autocorrelation to the rank of a centred transition matrix. They test the model across several settings: a six‑fold rolling (walk‑forward) study on a decade of SPY (the S&P 500 ETF), a sector‑balanced 30‑ticker panel spanning ten Global Industry Classification Standard sectors, a transfer test using CRSP data from one decade to a later two‑year slice, and a six‑asset equity basket. In these tests the rank bound was not active once they used a few latent states. Instead, increasing the flexibility of the per‑regime distributions (allowing heavy tails) closed most of the remaining gap in matching observed kurtosis and volatility clustering.