What is the method used to separate a time series into its seasonal, trend, and irregular components?

The method used to separate a time series into its seasonal, trend, and irregular components is known as time series decomposition. This approach allows analysts to break down a time series into its constituent parts to better understand the underlying patterns in the data.

Time series decomposition involves identifying and isolating the different components of a time series, which typically include:

1. Trend: The long-term movement or direction in the data over time.
2. Seasonal: The repeating variations or cycles in the data that occur at regular intervals, often correlated with seasons or specific time periods.
3. Irregular: The random, unpredictable fluctuations that cannot be attributed to either trend or seasonal factors.

By decomposing a time series, analysts can gain insights into the effects of these components separately, which can be particularly useful for forecasting and data analysis. This method improves the accuracy of predictions and helps in making informed decisions based on the identified patterns.

Other options like time series smoothing and forecasting relate to techniques for analyzing time series but do not specifically refer to the separation of the components. Time series analysis encompasses a broader range of methodologies, while time series forecasting focuses on predicting future values based on past data without explicitly breaking it down into components.