Explanation

Perfect multicollinearity occurs in scenario IV only.

Analysis of each scenario:

I. Only one seasonal dummy that is equal to 1

• This creates a single dummy variable
• No multicollinearity issue since there's only one variable

II. A holiday variation variable that accounts for an "Easter dummy variable"

• This is a single dummy variable for Easter
• No multicollinearity issue

III. A trading-day variation variable for modeling trading volume throughout the year

• This is typically a continuous variable or multiple dummies
• No inherent multicollinearity

IV. A dummy variable for each season, plus an intercept

• This creates perfect multicollinearity
• If you have 4 seasons and create 4 dummy variables plus an intercept, the sum of all dummy variables equals 1 (the constant vector)
• This creates a linear dependency: D₁ + D₂ + D₃ + D₄ = 1
• The intercept is perfectly collinear with the sum of the dummy variables

Solution to avoid multicollinearity:

• Either omit one dummy variable (use 3 dummies + intercept)
• Or omit the intercept and use all 4 dummies

This is known as the dummy variable trap.