Which statement is true regarding exponential smoothing where w is the smoothing parameter?

The statement that comparing the sum of squared errors (SS(w)) for different values helps choose the optimal smoothing parameter (w) is accurate. Exponential smoothing is a time series forecasting method that applies decreasing weights to past observations, with the most recent observations receiving the highest weights. The choice of the smoothing parameter significantly affects the forecast's responsiveness to changes in the data; hence, testing different values of w and evaluating the corresponding SS(w) allows practitioners to identify the value that minimizes error, leading to better forecasting performance.

Looking at the alternative options, w=1 indeed leads to no smoothing as it reflects using the latest value without considering previous observations. However, while it’s a valid observation regarding smoothing, it does not address the broader application of optimization through comparison of SS(w). The statement about smoothed estimates being referred to as discounted least squares estimates is also not accurate in the context of exponential smoothing; rather, they are simply referred to as smoothed estimates. This reinforces why the optimal choice is identifying the process of evaluating SS(w) against varying w to derive the most suitable parameter for exponential smoothing.