mean-reversion

Name: mean-reversion
Author: agiprolabs

223installs53forks

How to install mean-reversion?

agiprolabs/claude-trading-skills/mean-reversion

$npx -y skills add agiprolabs/claude-trading-skills --skill mean-reversion

Installs into the current project.

Summary

Mean-reversion strategy tools including Hurst exponent, half-life estimation, z-score signals, ADF testing, and Ornstein-Uhlenbeck modeling

Files · 1

View on GitHub

SKILL.md

1	# Mean Reversion
2
3	Mean reversion is the statistical tendency for prices, spreads, or other financial variables to return toward a long-run average after deviating from it. A mean-reverting series overshoots its mean, then corrects back -- creating predictable oscillations that can be traded.
4
5	## When Mean Reversion Works
6
7	- Ranging markets: Sideways price action with clear support/resistance
8	- Pairs spreads: Spread between cointegrated assets reverts to equilibrium
9	- Oversold/overbought extremes: RSI, Bollinger Band, or z-score extremes in stationary series
10	- Funding rate arbitrage: Perpetual funding rates revert to baseline
11	- Stablecoin depegs: Classic mean-reversion opportunity (peg = known mean)
12	- Post-dump recovery: Brief mean-reversion windows after initial PumpFun dumps
13
14	## When Mean Reversion Fails
15
16	- Strong trending markets (most crypto most of the time)
17	- Regime changes: what was stationary becomes non-stationary
18	- Structural breaks: token migration, protocol upgrade, delistings
19	- Low liquidity: wide spreads consume mean-reversion profits
20
21	---
22
23	## Testing for Mean Reversion
24
25	Before trading mean reversion, you must statistically confirm the series is mean-reverting. Three complementary tests:
26
27	### 1. Augmented Dickey-Fuller (ADF) Test
28
29	Tests the null hypothesis that a series has a unit root (non-stationary).
30
31	```python
32	from scipy import stats
33	import numpy as np
34
35	def adf_test(series: np.ndarray, max_lag: int = 0) -> dict:
36	"""Run ADF test. Reject null (p < 0.05) → stationary → mean-reverting."""
37	# See references/statistical_tests.md for full implementation
38	# Use statsmodels.tsa.stattools.adfuller for production
39	pass
40	```
41
42	- p < 0.01: Strong evidence of stationarity
43	- p < 0.05: Evidence of stationarity
44	- p > 0.10: Cannot reject unit root -- likely non-stationary
45
46	### 2. Hurst Exponent
47
48	Measures the long-range dependence of a time series.
49
50	\| Hurst Value \| Interpretation \| Trading Implication \|
51	\|-------------\|---------------\|---------------------\|
52	\| H < 0.5 \| Mean-reverting \| Trade mean reversion \|
53	\| H = 0.5 \| Random walk \| No edge \|
54	\| H > 0.5 \| Trending \| Trade momentum \|
55
56	```python
57	def hurst_exponent(series: np.ndarray) -> float:
58	"""Compute Hurst exponent via R/S method. H < 0.5 → mean-reverting."""
59	# See references/statistical_tests.md for full R/S algorithm
60	pass
61	```
62
63	### 3. Variance Ratio Test
64
65	Compares variance of multi-period returns to single-period variance.
66
67	- VR < 1: Negative autocorrelation (mean-reverting)
68	- VR = 1: Random walk
69	- VR > 1: Positive autocorrelation (trending)
70
71	```python
72	def variance_ratio(series: np.ndarray, q: int = 5) -> float:
73	"""Compute variance ratio at horizon q. VR < 1 → mean-reverting."""
74	returns = np.diff(np.log(series))
75	var_1 = np.var(returns)
76	returns_q = np.diff(np.log(series[::q]))
77	var_q = np.var(returns_q)
78	return var_q / (q * var_1)
79	```
80
81	See `references/statistical_tests.md` for complete implementations and interpretation guides.
82
83	---
84
85	## Half-Life Estimation
86
87	The half-life tells you how many periods it takes for a deviation to decay to half its size. This is the single most important parameter for mean-reversion trading.
88
89	### AR(1) Regression Method
90
91	Fit the autoregressive model: `delta_X_t = alpha + beta * X_{t-1} + epsilon`
92
93	```python
94	def half_life(series: np.ndarray) -> float:
95	"""Estimate mean-reversion half-life from AR(1) regression.
96
97	Returns:
98	Half-life in periods. Negative means non-mean-reverting.
99	"""
100	y = np.diff(series)
101	x = series[:-1]
102	x = np.column_stack([np.ones(len(x)), x])
103	beta = np.linalg.lstsq(x, y, rcond=None)[0][1]
104	if beta >= 0:
105	return -1.0 # Not mean-reverting
106	return -np.log(2) / np.log(1 + beta)
107	```
108
109	### Using Half-Life
110
111	\| Parameter \| Rule of Thumb \|
112	\|-----------\|--------------\|
113	\| Lookback window \| 2x half-life \|
114	\| Holding period \| 1x half-life \|
115	\| Maximum hold \| 3x half-life (stop) \|
116	\| Signal recalc \| 0.5x half-life \|
117
118	---
119
120	## Z-Score Signal Framework
121
122	The z-score normalizes the deviation from the mean, providing standardized entry/exit signals.
123
124	```
125	z = (price - rolling_mean) / rolling_std
126	```
127
128	### Signal Rules
129
130	\| Condition \| Signal \| Action \|
131	\|-----------\|--------\|--------\|
132	\| z < -2.0 \| Buy \| Enter long (price below mean) \|
133	\| z > +2.0 \| Sell \| Enter short (price above mean) \|
134	\| z crosses 0 \| Exit \| Close position (returned to mean) \|
135	\| abs(z) > 3.0 \| Stop \| Close position (reversion failed) \|
136
137	### Lookback Window
138
139	Set the rolling window to approximately 2x the half-life:
140
141	```python
142	def z_score_signals(
143	prices: np.ndarray,
144	lookback: int,
145	entry_z: float = 2.0,
146	exit_z: float = 0.0,
147	stop_z: float = 3.0,
148	) -> np.ndarray:
149	"""Generate z-score-based m

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mean-reversion

223installs53forks

View on GitHub

How to install mean-reversion?

agiprolabs/claude-trading-skills/mean-reversion

$npx -y skills add agiprolabs/claude-trading-skills --skill mean-reversion

Installs into the current project.

Summary

Mean-reversion strategy tools including Hurst exponent, half-life estimation, z-score signals, ADF testing, and Ornstein-Uhlenbeck modeling

Files · 1

View on GitHub

SKILL.md

1	# Mean Reversion
2
3	Mean reversion is the statistical tendency for prices, spreads, or other financial variables to return toward a long-run average after deviating from it. A mean-reverting series overshoots its mean, then corrects back -- creating predictable oscillations that can be traded.
4
5	## When Mean Reversion Works
6
7	- Ranging markets: Sideways price action with clear support/resistance
8	- Pairs spreads: Spread between cointegrated assets reverts to equilibrium
9	- Oversold/overbought extremes: RSI, Bollinger Band, or z-score extremes in stationary series
10	- Funding rate arbitrage: Perpetual funding rates revert to baseline
11	- Stablecoin depegs: Classic mean-reversion opportunity (peg = known mean)
12	- Post-dump recovery: Brief mean-reversion windows after initial PumpFun dumps
13
14	## When Mean Reversion Fails
15
16	- Strong trending markets (most crypto most of the time)
17	- Regime changes: what was stationary becomes non-stationary
18	- Structural breaks: token migration, protocol upgrade, delistings
19	- Low liquidity: wide spreads consume mean-reversion profits
20
21	---
22
23	## Testing for Mean Reversion
24
25	Before trading mean reversion, you must statistically confirm the series is mean-reverting. Three complementary tests:
26
27	### 1. Augmented Dickey-Fuller (ADF) Test
28
29	Tests the null hypothesis that a series has a unit root (non-stationary).
30
31	```python
32	from scipy import stats
33	import numpy as np
34
35	def adf_test(series: np.ndarray, max_lag: int = 0) -> dict:
36	"""Run ADF test. Reject null (p < 0.05) → stationary → mean-reverting."""
37	# See references/statistical_tests.md for full implementation
38	# Use statsmodels.tsa.stattools.adfuller for production
39	pass
40	```
41
42	- p < 0.01: Strong evidence of stationarity
43	- p < 0.05: Evidence of stationarity
44	- p > 0.10: Cannot reject unit root -- likely non-stationary
45
46	### 2. Hurst Exponent
47
48	Measures the long-range dependence of a time series.
49
50	\| Hurst Value \| Interpretation \| Trading Implication \|
51	\|-------------\|---------------\|---------------------\|
52	\| H < 0.5 \| Mean-reverting \| Trade mean reversion \|
53	\| H = 0.5 \| Random walk \| No edge \|
54	\| H > 0.5 \| Trending \| Trade momentum \|
55
56	```python
57	def hurst_exponent(series: np.ndarray) -> float:
58	"""Compute Hurst exponent via R/S method. H < 0.5 → mean-reverting."""
59	# See references/statistical_tests.md for full R/S algorithm
60	pass
61	```
62
63	### 3. Variance Ratio Test
64
65	Compares variance of multi-period returns to single-period variance.
66
67	- VR < 1: Negative autocorrelation (mean-reverting)
68	- VR = 1: Random walk
69	- VR > 1: Positive autocorrelation (trending)
70
71	```python
72	def variance_ratio(series: np.ndarray, q: int = 5) -> float:
73	"""Compute variance ratio at horizon q. VR < 1 → mean-reverting."""
74	returns = np.diff(np.log(series))
75	var_1 = np.var(returns)
76	returns_q = np.diff(np.log(series[::q]))
77	var_q = np.var(returns_q)
78	return var_q / (q * var_1)
79	```
80
81	See `references/statistical_tests.md` for complete implementations and interpretation guides.
82
83	---
84
85	## Half-Life Estimation
86
87	The half-life tells you how many periods it takes for a deviation to decay to half its size. This is the single most important parameter for mean-reversion trading.
88
89	### AR(1) Regression Method
90
91	Fit the autoregressive model: `delta_X_t = alpha + beta * X_{t-1} + epsilon`
92
93	```python
94	def half_life(series: np.ndarray) -> float:
95	"""Estimate mean-reversion half-life from AR(1) regression.
96
97	Returns:
98	Half-life in periods. Negative means non-mean-reverting.
99	"""
100	y = np.diff(series)
101	x = series[:-1]
102	x = np.column_stack([np.ones(len(x)), x])
103	beta = np.linalg.lstsq(x, y, rcond=None)[0][1]
104	if beta >= 0:
105	return -1.0 # Not mean-reverting
106	return -np.log(2) / np.log(1 + beta)
107	```
108
109	### Using Half-Life
110
111	\| Parameter \| Rule of Thumb \|
112	\|-----------\|--------------\|
113	\| Lookback window \| 2x half-life \|
114	\| Holding period \| 1x half-life \|
115	\| Maximum hold \| 3x half-life (stop) \|
116	\| Signal recalc \| 0.5x half-life \|
117
118	---
119
120	## Z-Score Signal Framework
121
122	The z-score normalizes the deviation from the mean, providing standardized entry/exit signals.
123
124	```
125	z = (price - rolling_mean) / rolling_std
126	```
127
128	### Signal Rules
129
130	\| Condition \| Signal \| Action \|
131	\|-----------\|--------\|--------\|
132	\| z < -2.0 \| Buy \| Enter long (price below mean) \|
133	\| z > +2.0 \| Sell \| Enter short (price above mean) \|
134	\| z crosses 0 \| Exit \| Close position (returned to mean) \|
135	\| abs(z) > 3.0 \| Stop \| Close position (reversion failed) \|
136
137	### Lookback Window
138
139	Set the rolling window to approximately 2x the half-life:
140
141	```python
142	def z_score_signals(
143	prices: np.ndarray,
144	lookback: int,
145	entry_z: float = 2.0,
146	exit_z: float = 0.0,
147	stop_z: float = 3.0,
148	) -> np.ndarray:
149	"""Generate z-score-based m

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