Quantitative Research · BTC-USD

Market Regime Detection

7-State Gaussian Hidden Markov Model trained on hourly BTC/USDT data from Binance (asset_id 587). States ordered by mean log return — State 0 most bearish, State 6 most bullish.

BTC Price Coloured by Regime

Regime Summary

State	Label	Count	% Time	Ann. Return	Ann. Vol	Hrly Vol	Mean Range	Vol Chg	Sharpe
0	Grind Down	772	4.41%	-85.24%	92.03%	0.0098	0.0218	+0.529	-92.6
1	Capitulation	2,831	16.16%	-23.71%	25.34%	0.0027	0.0070	-0.007	-93.6
2	Mild Bear	3,714	21.20%	-12.14%	14.78%	0.0016	0.0041	-0.065	-82.1
3	Sideways	2,704	15.43%	-1.73%	49.18%	0.0053	0.0102	-0.217	-3.5
4	Mild Bull	3,050	17.41%	+1.38%	11.99%	0.0013	0.0024	-0.029	+11.5
5	Bull	3,582	20.45%	+26.73%	16.19%	0.0017	0.0057	+0.020	+165.1
6	Rally	866	4.94%	+96.25%	60.77%	0.0065	0.0165	+0.530	+158.4

Ann. Return = Hourly log return × 8,760 · Ann. Vol = Hourly std × √8,760 · States sorted by mean return ascending

Regime Descriptions

State 0: Grind Down

Persistent grinding downtrend. Prices bleed lower slowly each hour.

·Consistent small negative returns
·Low intra-bar range (0.49%)
·Falling volume

State 1: Capitulation

Flash crashes and panic sell-offs. Wild price oscillations trending down.

·Massive intra-bar range (2.4%)
·High volume surges
·Wild price swings

State 2: Mild Bear

Moderate negative drift. Typical correction phases or uncertain macro.

·Slightly negative mean return
·Moderate range (1.0%)
·Above-average volume

State 3: Sideways

Consolidation. Near-zero returns, tightest range, lowest volume.

·Near-zero hourly return
·Tightest range (0.24%)
·Flat/falling volume

State 4: Mild Bull

Moderately positive drift. Recoveries and early-stage uptrends.

·Positive mean return (+0.034%/hr)
·Moderate range (1.2%)
·Declining volume

State 5: Bull

Steady low-volatility uptrend. BTC climbs consistently. Sharpe of 165.

·Consistent positive returns
·Low range (0.66%)
·Decreasing volume (-38%)

State 6: Rally

Mirror of Grind Down. Strong persistent uptrend. Sharpe +158.

·Strongest positive mean return
·Low range (0.47%)
·Stable volume

How Hidden Markov Models Work

The Core Idea

A Hidden Markov Model assumes markets exist in a small number of unobservable hidden states. You cannot see the state directly — only its noisy effects in price and volume.

P(state[t+1] | state[t]) → Transition Matrix (7×7)

P(obs | state) → Gaussian Emission

P(state[0]) → Initial Distribution

Gaussian Emissions — 3 Features

Log Return

log(Closeₜ / Closeₜ₋₁)

Normally distributed, captures direction & magnitude

Price Range

(High − Low) / Close

Intra-bar volatility, normalised for price level

Volume Change

log(Volₜ / Volₜ₋₁)

Liquidity shifts; log ratio avoids sign asymmetry

Training: Baum-Welch (EM)

E-stepForward-backward algorithm computes state probabilities at each timestep given all observations.

M-stepUpdate transition matrix and Gaussian means/covariances to maximise expected log-likelihood.

RepeatUntil convergence (Δlog-likelihood < 1e-4). Converged in ~100 iterations.

Decoding: Viterbi Algorithm

Each bar is assigned a regime using the Viterbi algorithm — dynamic programming that finds the most probable hidden state sequence.

n_components = 7 states

covariance_type = "full"

n_iter = 100 · random_state = 42