Financial Risk Manager Part 1

Explanation

The model is given as:

$y_t = 0.2 \times \text{Time}_t + 10.5 + 3.0 \times D_{2t} + 5.4 \times D_{3t} + 0.7 \times D_{4t}$

Step 1: Determine the Time Period

• The model starts in May 2019
• $y_{(T+1)}$ refers to June 2019
• We need to find September 2020

From June 2019 to September 2020:

• June 2019 to May 2020 = 12 months
• June 2020 to September 2020 = 4 months
• Total = 16 months

So September 2020 = $y_{(T+16)}$

Step 2: Identify the Seasonal Component

From the seasonal table:

• September falls under Fall season
• Fall season uses dummy variable $D_{4t}$

Therefore, for September 2020:

• $D_{2t} = 0$ (not Spring)
• $D_{3t} = 0$ (not Summer)
• $D_{4t} = 1$ (Fall season)

Step 3: Calculate the Prediction

$y_{(T+16)} = 0.2 \times 16 + 10.5 + 3.0 \times 0 + 5.4 \times 0 + 0.7 \times 1$ $y_{(T+16)} = 3.2 + 10.5 + 0 + 0 + 0.7$ $y_{(T+16)} = 14.4$

Since housing starts are given in thousands, the model predicts approximately 14 housing starts in September 2020.

Key Points:

• The intercept (10.5) represents the baseline for Winter season
• Seasonal dummies add to this baseline for their respective seasons
• The trend component (0.2 × Time) captures the linear growth over time