MARKET REGIMES / MARKOV-SWITCHING · SEPTEMBER 2026
Bitcoin Volatility: A Markov Regime Analysis
Recent daily returns fit the low-volatility state more closely. A two-state model tracks shifts between calmer and more turbulent conditions. A three-state comparison shows that some probability still sits in the middle-volatility state.
Low-volatility probability · Sep 13 close
%
Binance BTC/USDT · UTC daily candles · Data through Sep 13, 2026. State probabilities estimate current volatility conditions; they do not measure the chance of a future price rise.
01 / The year in market regimes
Each dot marks a daily close, colored by the most likely state given that day’s return. Prices and volatility regimes share the same timeline.
2026 closing prices and two-state classifications
Mint: low volatility. Amber: high volatility. January–June is a retrospective view using parameters fitted over that period. From July onward, parameters stay fixed and probabilities update daily. The classification threshold is 50%; the full probability series appears below.
02 / Recent shifts in state probabilities
From July onward, state probabilities use only returns observed up to that day. Classifications can flip when probabilities sit near the threshold. The full probability trajectory makes that uncertainty visible.
Out-of-sample state probabilities
At the latest completed daily close, the low-volatility probability was %. It had been the more likely state for consecutive days. The closing price was USDT, a 30-day change of %. Cumulative price gains can coexist with smaller recent daily moves: the 30-day return and the current volatility state describe different aspects of the market.
At the latest completed daily close, the low-volatility probability was
%. It had been the more likely state for
consecutive days. The closing price was
USDT, a 30-day change of
%. Cumulative price gains can coexist with smaller recent daily moves: the 30-day return and the current volatility state describe different aspects of the market.
OHLC: the latest 30 completed days
03 / How the model identifies volatility regimes
The model assumes that markets move between states that cannot be observed directly. Each state has its own mean daily return and volatility. Transition probabilities describe how persistent the states are. All parameters are estimated from historical returns.
Fitted return distributions by state
These Gaussian distributions use parameters fitted to the training period. The narrow curve concentrates on small daily moves; the wider curve allows larger moves in either direction. They show fitted distributions, rather than a histogram of observed returns.
Daily return = 100 × ln(today’s close ÷ yesterday’s close). The model estimates each state’s mean return, variance and next-day transition probabilities. Each new daily return then updates the estimated probability of each state.
Both fitted states have mean returns close to zero. Their main difference is volatility, which gives them their names: low and high volatility. The high-volatility state includes large gains and losses, so its probability alone gives no buy or sell direction.
Training period: Jan 2, 2022–Jun 30, 2026, with daily returns. Holdout period: Jul 1–Sep 13, 2026, with days. Weekends are included; incomplete UTC daily candles are excluded.
Training period: Jan 2, 2022–Jun 30, 2026, with
daily returns. Holdout period: Jul 1–Sep 13, 2026, with
days. Weekends are included; incomplete UTC daily candles are excluded.
Two-state model parameters
| State | Mean daily return (%) (percent) | Daily return SD (%) (percent) | Next-day persistence (%) (percent) | Expected duration (days) |
|---|---|---|---|---|
| 低波动 | 0.0356 | 1.5256 | 83.1646 | 5.9399 |
| 高波动 | -0.0407 | 4.2958 | 61.0029 | 2.5643 |
04 / State persistence and transitions
The transition matrix shows the conditional probability of staying in a state or switching the next day. Diagonal cells indicate persistence; off-diagonal cells indicate a switch. These estimates describe persistence in the training sample.
Daily state transition probabilities
Expected duration is 1 ÷ (1 − the probability of staying in the same state), assuming constant transition probabilities. Actual episodes can be shorter or longer. Elapsed days cannot simply be subtracted from this expectation to estimate the time remaining.
05 / Sensitivity to the number of states
Adding a state changes the classification boundaries. The three-state model has a lower training BIC; the two-state model has a slightly higher mean predictive log score over this holdout period. These differences do not establish a consistently better model.
Current probabilities: three-state model
Model comparison
Lower BIC and higher mean predictive log scores are better. The log score evaluates the density assigned to observed returns, rather than directional accuracy. The three-state model defines a narrower low-volatility state, so subtracting its probability from the two-state estimate would not measure a change in confidence.
Both models currently assign most of their probability to their lower-volatility states. They broadly agree that recent large daily moves have eased. The precise state and probability still depend on how finely the model divides the market and on its assumptions.
| Model | Training BIC | Holdout mean log score |
|---|---|---|
| 2 状态 | 7597.52 | -1.9836 |
| 3 状态 | 7591.23 | -1.988 |
Scope and sources
This report presents a reproducible method for identifying volatility regimes. Constant transition probabilities and Gaussian returns are simplifying assumptions; extreme moves, changes in market structure and day-of-week effects may affect the results. ETF flows, derivatives leverage and macroeconomic variables are outside the model. The analysis does not establish what caused market moves or validate a profitable trading strategy.
Reproducibility details
Data: Binance Spot BTCUSDT daily candles. Model: statsmodels 0.15.0 MarkovRegression, with switching means and variances. Each two-state and three-state specification uses three random seeds and multiple starting values; the converged fit with the highest likelihood is retained. Probabilities are filtered with training parameters held fixed. Out-of-sample scores use daily conditional log likelihoods. Data and computed results are frozen for this edition.
Price data: Binance Spot Klines · Method: statsmodels MarkovRegression . Retrieved Sep 14, 2026 UTC. BTC/USDT is a stablecoin-denominated quote from a single exchange.
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