Hurst exponent evaluation and R/S-analysis

# hurst

## Hurst exponent evaluation and R/S-analysis

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.

## Usage

Install hurst module with

```pip install hurst
```

or

```pip install -e https://github.com/Mottl/hurst
```
```import matplotlib.pyplot as plt
import numpy as np
import matplotplotlib.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`

## 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)`