Time Series • Time Series Analysis and Components

P2.07 Logarithmic Transformation

Practical 2 Time Series Analysis and Components

Quick concept

A positive series grows with increasing variation. Compare the original plot with a log plot and explain when a log is helpful.

Practical / Solution

P2.07 Logarithmic Transformation

Problem Statement

A positive series grows with increasing variation. Compare the original plot with a log plot and explain when a log is helpful.

Learning Outcomes

Apply a log transform to positive data.
Explain that logs can stabilise relative growth.

Hint

Use np.log on strictly positive values. Do not log zeros or negatives.

Theory

Transformations can stabilise variance or make growth more linear. A logarithm turns multiplicative growth into additive growth. It is not always required.

Dataset / Data Source

Constructed positive series: 20, 24, 30, 38, 50, 66, 90, 125.

Analysis / Program

import pandas as pd import numpy as np import matplotlib.pyplot as plt y = pd.Series([20, 24, 30, 38, 50, 66, 90, 125]) fig, axes = plt.subplots(1, 2, figsize=(9, 4)) y.plot(ax=axes[0], marker="o", title="Original") np.log(y).plot(ax=axes[1], marker="o", title="Log") plt.tight_layout() plt.show()

Expected Output

Two plots: original curve steepening upward, log series closer to a straight rise.

Result / Interpretation

If variation grows with the level, a log scale can make the pattern easier to model. Forecasts on the log scale must be converted back carefully.

Note

Use a log only for positive data, and interpret results on the original scale when the decision uses original units.