Exponential Smoothing on a Random Walk

smoothing.py

from typing import Iterable

import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns

from numpy import ndarray

def generate_random_walk(size: int) -> ndarray:
    draw = np.random.random(size)
    steps = np.where(draw > 0.5, 1, -1)
    return np.cumsum(steps)

# taken/inspired from: https://stackoverflow.com/a/42926270/12160601
def exponential_smoothing(arr: ndarray, window: int) -> ndarray:
    a = 2 / (window + 1.0)
    n = len(arr)
    
    powers = (1 - a) ** np.arange(n + 1)
    scale = 1 / powers[:-1]
    offset = arr[0] * powers[1:]
    pw0 = a * (1 - a) ** (n - 1)
    
    mult = arr * pw0 * scale
    return offset + np.cumsum(mult) * scale[::-1]

def plot_trends(trends: Iterable[ndarray], labels: Iterable[str], **kwargs):
    fig, ax = plt.subplots(figsize=(8, 5))
    styles = {
        'linewidth': 2,
    }
    ax.axhline(0, linestyle='--', color='black')
    
    for t, l in zip(trends, labels):
        n = len(t)
        ax.plot(np.arange(n), t, label=l, **styles)
    
    xlabel = kwargs.get('xlabel', 'X')
    ylabel = kwargs.get('ylabel', 'Y')
    title = kwargs.get('title', 'Trends')
    
    ax.legend()
    ax.grid(linestyle=':')
    ax.set_xlabel(xlabel)
    ax.set_ylabel(ylabel)
    ax.set_title(title)
    sns.despine()
    fig.tight_layout()
    plt.show()

Some example usage (assuming the imports from above have been called)

# matplotlib plot style defaults
sns.set(style='white', font_scale=1.3)

walk = generate_random_walk(5000)
walk_smooth = exponential_smoothing(walk, window=20)

config = {
    'xlabel': 'Steps',
    'ylabel': 'Units',
    'title': 'Random Walk\n(with Exponential Smoothing)',
}
plot_trends([walk, walk_smooth], ['Random Walk', 'Exponential Smoothing'], **config)