What is the forecasting method that computes a weighted average of the most recent k data values in the time series?

The weighted moving average method is the forecasting approach that involves calculating the average of the most recent k data values in a time series while applying different weights to each value. This method is particularly useful when recent observations are considered more relevant or informative than older ones. By assigning greater weights to the most current data points, the weighted moving average can provide a more responsive forecast compared to a simple moving average, which treats all values equally.

This technique is beneficial in environments with trends or seasonal variations, where reflecting the latest data can enhance the accuracy of the forecast. It allows forecasters to adjust the significance of older data points dynamically, depending on how much impact they wish them to exert on the predictions.

Other methods listed, such as simple moving averages, do not apply weights, while exponential smoothing incorporates all past data but does so through a smoothing constant rather than individual weights for a specified number of recent observations. Time series regression, on the other hand, is a different analytical method that models the relationship between time series data and time itself, rather than using averages of data points. Thus, the weighted moving average method stands out as the correct answer due to its unique application of weighted data in calculations.