Question

in a moving average forecast, as the value of k select , the forecast reacts slowly to recent changes in the time seri select , the forecast reacts more qui (dropdown options: increases, stabilizes, stays the same, decreases)

Explanation:

In a moving average forecast, \( k \) represents the number of periods used to calculate the average. When \( k \) increases, we are averaging more periods, so the forecast is less responsive to recent changes (reacts slowly). When \( k \) decreases, we are averaging fewer periods, so the forecast is more responsive to recent changes (reacts quickly).

For the first blank (where the forecast reacts slowly to recent changes): As \( k \) increases, the moving average includes more past data, so it smooths out recent fluctuations, leading to a slower reaction to recent changes.

For the second blank (where the forecast reacts more quickly): As \( k \) decreases, the moving average includes fewer past data points, so it is more influenced by recent data, leading to a quicker reaction to recent changes.

Answer:

First blank: increases
Second blank: decreases