Financial Risk Manager Part 1

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An investment analyst wants to fit the weekly sales (in millions) of his company by using the sales data from Jan 2018 to Feb 2019. The regression equation is defined as:

\ln Y_t = 5.105 + 0.044t, \quad t = 1, 2, ..., 100

What is the trend value estimate of the sales in the $90^{th}$ week?_

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TTanishq

8,647.28 Million

7,947.26 Million

8,537.38 Million

8,237.48 Million

Explanation:

From the regression equation, $\hat{\beta}_0 = 5.105$ and $\hat{\beta}_1 = 0.044$ . We know that, under log-linear trend models, the predicted trend value is given by:

\ln Y_t = \hat{\beta}_0 + \hat{\beta}_1 t \\ \Rightarrow Y_t = e^{\hat{\beta}_0 + \hat{\beta}_1 t} \\ \therefore Y_{90} = e^{5.105 + 0.044 \times 90} \\ = e^{5.105 + 3.96} \\ = e^{9.065} \\ = 8,647.28 \text{ Million} $$_

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