Recall the seasonal decomposition method in a time-series analysis we did in lecture. We computed the seasonal index for each quarter. This steps allows us to:

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In seasonal decomposition of a time series, we typically aim to separate the components: trend, seasonal, and irregular. This framing guides how we interpret the seasonal indices.
Option 1: 'Remove the seasonality from the data and estimate the trend' — this aligns with the classic additive (or multiplicative) decomposition procedure, where once seasonal effects are quantified via seasonal indices, we can deseasonalize the data to estimate the underlying trend.
Option 2: 'Remove the period from the data and estimate the seasonality.' In time series terminology, we do not remove the period; the period is the length of the cycle (e.g., quarters), not something we remove to estimate seasonality. This misstates the objective of constructing seasonal indices.
Option 3: 'Remove the trend from the data and estimate the seasonality.' While detrending can be part of some analyses, the standard seasonal decomposition first uses seasonal indices to model seasonality and then can interpret the remaining data as trend plus irregular. Saying we remove the trend to estimate seasonality is not the typical objective and can be misleading about the method.
Option 4: 'Identify all the seasons.' The seasonal indices quantify how each season (quarter) differs from the average, but the goal isn't merely identifying seasons themselves; it’s quantifying their average effect and enabling deseasonalized data. This describes recognition rather than estimation of the seasonal pattern itself in the decomposition context.
Option 5: 'Convert the data from a quarterly time series to an annual time series data.' Seasonal decomposition does not convert quarterly data to annual data; it separates components within the quarterly structure to analyze underlying patterns, not collapses the frequency.
Overall, the statement that matches the standard purpose of computing seasonal indices in decomposition is to remove seasonality and estimate the trend, which helps reveal the underlying movement in the data without seasonal fluctuations.

Recall the seasonal decomposition method in a time-series analysis we did in lecture. We computed the seasonal index for each quarter. This steps allows us to:

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