QQQ Hidden Markov Regime Model

Model inputs + parameters drag the chart to set training range

Hidden states (K)

EM iterations (max)

Random restarts

Train from

Train to

Display window

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Observation variables in this window

1-day log return r_t = ln(C_t / C_{t-1}). Daily log return of QQQ — separates regimes by drift.
5-day log realized volatility log RV_t = log of the stdev of the last 5 daily log returns. Captures volatility clustering — bear regimes have systematically higher RV (Bulla & Bulla 2006; Nystrup et al. 2017).

Each bar's emission is the joint vector of the selected variables, modeled per-regime as a multivariate Gaussian with full covariance. Toggle variables and click Retrain to refit. The HMM structure card below always reflects the currently selected configuration.

Current regime latest bar

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Last bar

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Trained

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Bars used

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Log-likelihood

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Learned emission parameters per-state distribution

Metric	LONG	SHORT

Transition matrix today → tomorrow

→ LONG

→ SHORT

LONG →

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SHORT →

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rows = today · cols = tomorrow · each row sums to 1.00

QQQ price · regime shading scroll to zoom · drag to pan · click reset

scroll · pinch to zoom · drag to pan · hover for per-bar detail

Regime probability ribbon P(state) per day · smoothed

HMM structure awaiting training…

References

Baum, Leonard E., Ted Petrie, George Soules, and Norman Weiss. "A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chains." The Annals of Mathematical Statistics 41, no. 1 (1970): 164–171.
Viterbi, Andrew J. "Error Bounds for Convolutional Codes and an Asymptotically Optimum Decoding Algorithm." IEEE Transactions on Information Theory 13, no. 2 (1967): 260–269.
Wang, Matthew, Yi-Hong Lin, and Ilya Mikhelson. "Regime-Switching Factor Investing with Hidden Markov Models." Journal of Risk and Financial Management 13, no. 12 (2020): 311. https://doi.org/10.3390/jrfm13120311.
Yuan, Yuan, and Gautam Mitra. "Market Regime Identification Using Hidden Markov Models." SSRN Working Paper, 2019. https://ssrn.com/abstract=3406068.
Bulla, Jan, and Ingo Bulla. "Stylized Facts of Financial Time Series and Hidden Semi-Markov Models." Computational Statistics & Data Analysis 51, no. 4 (2006): 2192–2209. https://doi.org/10.1016/j.csda.2006.07.021.
Nystrup, Peter, Henrik Madsen, and Erik Lindström. "Long Memory of Financial Time Series and Hidden Markov Models with Time-Varying Parameters." Journal of Forecasting 36, no. 8 (2017): 989–1002. https://doi.org/10.1002/for.2447.

QQQ · Hidden Markov Model