Answer-first summary for fast verification
Answer: 0.058
## 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:** 1. The MA(1) model depends only on current and lagged shocks, not on lagged realizations 2. Yesterday's realization (0.015) is not used in the MA(1) calculation - it's extraneous information 3. The calculation is straightforward: current shock plus theta times lagged shock 4. The negative lagged shock (-0.160) reduces the current realization
Author: Nikitesh Somanthe
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Assume the shock in a time series is approximated by Gaussian white noise. Yesterday's realization, was 0.015 and the lagged shock was -0.160. Today's shock is 0.170. If the weight parameter theta, , is equal to 0.70, determine today's realization under a first-order moving average, MA(1), process.
A
0.254
B
0.075
C
0.062
D
0.058
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