Financial Risk Manager Part 1

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Consider the time series $Y_t = 1 + 0.5t + Z_t$ where $Z_t \sim WN(0,1)$ . Determine the mean function of $Y_t$ .

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NNikitesh

Last updated: February 2, 2026 at 10:22

$0.5t$

$1$

$1 + 0.5t$

$1.5$

Explanation:

The mean function of $Y_t$ is calculated as follows:

$\mu_Y(t) = E(Y_t) = E(1 + 0.5t + Z_t)$

Since $1 + 0.5t $is deterministic (non-random), and$ Z_t \sim WN(0,1) $where$ WN$ stands for White Noise with mean 0 and variance 1:

$\mu_Y(t) = 1 + 0.5t + E(Z_t)$

Given that $E(Z_t) = 0$ :

$\mu_Y(t) = 1 + 0.5t$

Therefore, the correct answer is C: $1 + 0.5t$.

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