# hurst
## Hurst exponent evaluation and R/S-analysis
[](https://travis-ci.org/Mottl/hurst)
[](https://pypi.org/project/hurst/)
[](https://pepy.tech/project/hurst)
**hurst** is a small Python module for analysing __random walks__ and evaluating the __Hurst exponent (H)__.
H = 0.5 — Brownian motion,
0.5 < H < 1.0 — persistent behavior,
0 < H < 0.5 — anti-persistent behavior.
## Installation
Install **hurst** module with
`pip install hurst`
or
`pip install -e git+https://github.com/Mottl/hurst#egg=hurst`
## Usage
```python
import numpy as np
import matplotlib.pyplot as plt
from hurst import compute_Hc, random_walk
# Use random_walk() function or generate a random walk series manually:
# series = random_walk(99999, cumprod=True)
np.random.seed(42)
random_changes = 1. + np.random.randn(99999) / 1000.
series = np.cumprod(random_changes) # create a random walk from random changes
# Evaluate Hurst equation
H, c, data = compute_Hc(series, kind='price', simplified=True)
# Plot
f, ax = plt.subplots()
ax.plot(data[0], c*data[0]**H, color="deepskyblue")
ax.scatter(data[0], data[1], color="purple")
ax.set_xscale('log')
ax.set_yscale('log')
ax.set_xlabel('Time interval')
ax.set_ylabel('R/S ratio')
ax.grid(True)
plt.show()
print("H={:.4f}, c={:.4f}".format(H,c))
```
```H=0.4964, c=1.4877```
### Kinds of series
The `kind` parameter of the `compute_Hc` function can have the following values:
`'change'`: a series is just random values (i.e. `np.random.randn(...)`)
`'random_walk'`: a series is a cumulative sum of changes (i.e. `np.cumsum(np.random.randn(...))`)
`'price'`: a series is a cumulative product of changes (i.e. `np.cumprod(1+epsilon*np.random.randn(...)`)
## Brownian motion, persistent and antipersistent random walks
You can generate random walks with `random_walk()` function as following:
### Brownian
```brownian = random_walk(99999, proba=0.5)```
### Persistent
```persistent = random_walk(99999, proba=0.7)```
### Antipersistent
```antipersistent = random_walk(99999, proba=0.3)```
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"description": "# hurst\n## Hurst exponent evaluation and R/S-analysis\n\n\n\n[](https://travis-ci.org/Mottl/hurst)\n[](https://pypi.org/project/hurst/)\n[](https://pepy.tech/project/hurst)\n\n**hurst** is a small Python module for analysing __random walks__ and evaluating the __Hurst exponent (H)__.\n\nH = 0.5 \u2014 Brownian motion, \n0.5 < H < 1.0 \u2014 persistent behavior, \n0 < H < 0.5 \u2014 anti-persistent behavior. \n\n## Installation\nInstall **hurst** module with \n`pip install hurst` \nor \n`pip install -e git+https://github.com/Mottl/hurst#egg=hurst`\n\n## Usage\n```python\nimport numpy as np\nimport matplotlib.pyplot as plt\nfrom hurst import compute_Hc, random_walk\n\n# Use random_walk() function or generate a random walk series manually:\n# series = random_walk(99999, cumprod=True)\nnp.random.seed(42)\nrandom_changes = 1. + np.random.randn(99999) / 1000.\nseries = np.cumprod(random_changes) # create a random walk from random changes\n\n# Evaluate Hurst equation\nH, c, data = compute_Hc(series, kind='price', simplified=True)\n\n# Plot\nf, ax = plt.subplots()\nax.plot(data[0], c*data[0]**H, color=\"deepskyblue\")\nax.scatter(data[0], data[1], color=\"purple\")\nax.set_xscale('log')\nax.set_yscale('log')\nax.set_xlabel('Time interval')\nax.set_ylabel('R/S ratio')\nax.grid(True)\nplt.show()\n\nprint(\"H={:.4f}, c={:.4f}\".format(H,c))\n```\n\n![R/S analysis](https://github.com/Mottl/hurst/raw/master/examples/regression.png?raw=true \"R/S analysis\")\n\n```H=0.4964, c=1.4877```\n\n### Kinds of series\nThe `kind` parameter of the `compute_Hc` function can have the following values: \n`'change'`: a series is just random values (i.e. `np.random.randn(...)`) \n`'random_walk'`: a series is a cumulative sum of changes (i.e. `np.cumsum(np.random.randn(...))`) \n`'price'`: a series is a cumulative product of changes (i.e. `np.cumprod(1+epsilon*np.random.randn(...)`)\n\n## Brownian motion, persistent and antipersistent random walks\nYou can generate random walks with `random_walk()` function as following:\n\n### Brownian\n```brownian = random_walk(99999, proba=0.5)```\n\n\n![Brownian motion](https://github.com/Mottl/hurst/raw/master/examples/Brownian_motion.png?raw=true \"Brownian motion\")\n\n### Persistent\n```persistent = random_walk(99999, proba=0.7)```\n\n\n![Persistent random walk](https://github.com/Mottl/hurst/raw/master/examples/Persistent.png?raw=true \"Persistent random walk\")\n\n### Antipersistent\n```antipersistent = random_walk(99999, proba=0.3)```\n\n\n![Antipersistent random walk](https://github.com/Mottl/hurst/raw/master/examples/Antipersistent.png?raw=true \"Antipersistent random walk\")\n\n\n",
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