Final answer:
The value of F_{t+i} in basic exponential smoothing indicates the forecast for a future period, applying weights that decrease exponentially for older data.
Step-by-step explanation:
In the context of simple forecasting with basic exponential smoothing, the value of F_{t+i} would refer to the forecast for a future time period. The technique of exponential smoothing is used to forecast data by applying a weighting factor that decreases exponentially for older data, emphasizing more recent observations.
Now, considering the given references, the current falls to 0.3681 in the first interval, and then 0.368 of the remaining toward zero in each subsequent time interval. This is indicative of an exponential decay pattern. In a practical application for business or finance, this would resemble the discounted value of future payments or cash flows subject to a decay factor or discount rate over time t.
However, without the specific formula for the exponential smoothing, additional details of the smoothing constant \( \alpha \), and the previous period's forecast and observation, it is not possible to accurately calculate F_{t+i}. Typically, the forecast would be updated as new data becomes available, using the formula F_{t+1} = \alpha \cdot X_t + (1 - \alpha) \cdot F_t, where X_t is the most recent observation and \( \alpha \) is the smoothing constant.