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