Apprendre Understanding Moving Averages

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Moving averages are a foundational tool in time series analysis, especially for smoothing noisy data and making forecasts. The simple moving average (SMA) is one of the most basic and widely used types. An SMA is calculated by taking the arithmetic mean of a fixed number of consecutive observations in a time series. This rolling calculation helps to smooth out short-term fluctuations, making underlying trends and patterns easier to observe.

When you apply an SMA to a time series, you essentially create a new series where each value is the average of the previous n data points, where n is the window size. The main role of SMA in time series analysis is to reduce noise, making it easier to identify trends and cycles. This makes SMA a valuable tool for both data exploration and as a simple forecasting method, especially when you want to estimate the next value as the mean of recent observations.


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import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

# Generate a sample time series: daily values with random noise
np.random.seed(42)
dates = pd.date_range(start="2023-01-01", periods=50)
data = np.cumsum(np.random.randn(50)) + 10  # random walk

series = pd.Series(data, index=dates)

# Compute a simple moving average (window size = 5)
window_size = 5
sma = series.rolling(window=window_size).mean()

# Plot the original series and its moving average
plt.figure(figsize=(10, 5))
plt.plot(series, label="Original Series")
plt.plot(sma, label=f"SMA (window={window_size})", linewidth=2)
plt.title("Simple Moving Average Smoothing")
plt.xlabel("Date")
plt.ylabel("Value")
plt.legend()
plt.tight_layout()
plt.show()

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Section 1. Chapitre 2