Which method is primarily used to predict future values based on past observed values in a time series?

The correct choice focuses on forecasting methods, which are specifically designed to predict future values based on historical data. These methods analyze patterns, trends, and cycles in past observed values in a time series to make informed estimates about future occurrences.

Forecasting methods can include a range of tools and techniques such as moving averages, exponential smoothing, and various regression analyses that consider the underlying temporal structure of the data. By leveraging this historical data, forecasting methods provide a systematic approach to projecting future outcomes, which is a fundamental aspect of many quantitative business analyses.

In contrast, smoothing techniques aim to reduce the noise in a dataset to reveal underlying trends, but they do not predict future values on their own. Descriptive statistics summarize and describe the characteristics of a dataset but do not involve predictions. Causal analysis seeks to identify relationships and causal connections between variables, rather than focusing on predicting future values from past observations. Each of these other options plays important roles in data analysis but does not directly address the task of projecting future values from historical time series data like forecasting methods do.