Financial Risk Manager Part 1

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Assume the shock in a time series is approximated by Gaussian white noise. Yesterday's realization, $y_{(t)}$ was 0.015 and the lagged shock was -0.160. Today's shock is 0.170. If the weight parameter theta, $\theta$ , is equal to 0.70, determine today's realization under a first-order moving average, MA(1), process.

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NNikitesh

Last updated: February 2, 2026 at 10:22

0.254

0.075

0.062

0.058

Explanation:

Explanation

For an MA(1) process, the model is given by:

$y_t = \varepsilon_t + \theta \varepsilon_{t-1}$

Where:

$y_t$ = today's realization
$\varepsilon_t$ = today's shock (0.170)
$\varepsilon_{t-1}$ = yesterday's shock (-0.160)
$\theta$ = weight parameter (0.70)

Plugging in the values:

$y_t = 0.170 + 0.70 \times (-0.160)$ $y_t = 0.170 - 0.112$ $y_t = 0.058$

Key points:

The MA(1) model depends only on current and lagged shocks, not on lagged realizations
Yesterday's realization (0.015) is not used in the MA(1) calculation - it's extraneous information
The calculation is straightforward: current shock plus theta times lagged shock
The negative lagged shock (-0.160) reduces the current realization

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