In forecasting techniques, which method involves an iterative process of gathering and refining input?

The correct method that involves an iterative process of gathering and refining input is the Delphi method. This technique is specifically designed to harness the knowledge and insights of a group of experts over multiple rounds. By soliciting their opinions anonymously and providing feedback on the responses after each round, the Delphi method allows experts to revise their predictions or viewpoints based on the collective input of the group. This iterative refining process helps converge on a more accurate and reliable forecast.

In contrast, extrapolation relies on historical data trends without the iterative input from multiple sources, merely projecting future values based on past patterns. Leading indicators are economic indicators that typically precede changes in economic activity but do not involve the refinement of expert inputs. Expert judgment involves the evaluation of opinions from specialists but may not follow a structured iterative process like the Delphi method. Thus, the iterative nature and the emphasis on consensus building in the Delphi method set it apart as the most appropriate choice for this question.