Time Series • Time Series Analysis and Components

P2.04 Original vs Smoothed Series

Practical 2 Time Series Analysis and Components

Quick concept

Compare the original series with 3-month and 5-month moving averages and discuss the bias-smoothness trade-off.

Practical / Solution

P2.04 Original vs Smoothed Series

Problem Statement

Compare the original series with 3-month and 5-month moving averages and discuss the bias-smoothness trade-off.

Learning Outcomes

See that a longer window is smoother.
See that a longer window reacts more slowly.

Theory

A longer moving-average window removes more noise and more signal. There is no universally best window.

Dataset / Data Source

Same teaching series as P2.03, extended by repeating the comparison.

Analysis / Program

import pandas as pd import matplotlib.pyplot as plt idx = pd.date_range("2025-01-01", periods=12, freq="MS") y = pd.Series([10, 13, 11, 16, 15, 20, 18, 22, 21, 25, 24, 28], index=idx) y.plot(label="original") y.rolling(3, center=True).mean().plot(label="MA3") y.rolling(5, center=True).mean().plot(label="MA5") plt.legend() plt.tight_layout() plt.show()

Expected Output

One chart with three lines. MA5 is smoother and lags more than MA3.

Result / Interpretation

MA3 keeps more local detail. MA5 is easier to read as a trend but slower to show a genuine jump. Choice depends on the question.

Note

Smoothing is a display and exploration tool, not automatically a forecast model.