When using classical decompose(), how is the trend-cycle component typically estimated?

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BlackTom AI · Accepted Answer

To approach the question about how the trend-cycle component is typically estimated in classical decomposition, consider what each option implies about separating components in time series.
Option 1: 'By fitting a linear regression model.' In classical decomposition, the trend is generally not extracted by fitting a regression to the observed data as a whole; instead, the trend is commonly estimated using smoothing methods that emphasize gradual changes over time rather than a parametric fit to every data point. This makes this option less consistent with the standard decomposition procedure.
Option 2: 'By using a moving average smoother.' This aligns with classical additive or multiplicative decomposition methods, where a moving average (often a centered moving average) is employed to smooth out seasonal and irregular components, leaving an estimate of the underlying trend. This is a classic, widely taught approach.
Option 3: 'By applying a seasonal filter.' A seasonal filter targets extracting seasonality, not the broader trend-cycle component. While filtering can interact with seasonal elements, the explicit extraction of the trend-cycle typically uses smoothing to remove high-frequency fluctuations, not a seasonality-focused filter.
Option 4: 'By using loess smoothing.' Loess (local regression) is a flexible smoothing method used in some modern time-series analyses, but within the context of classical decomposition, the standard textbook method is a simpler moving average smoothing, not a loess fit. Therefore this option describes a more contemporary or alternative approach than the classical method.
In summary, among the listed options, the classic and conventional technique for estimating the trend-cycle in classical decomposition is to apply a moving average smoother, which reduces short-term fluctuations to reveal the long-term trend. The other methods either target different components (seasonality) or rely on more flexible, non-classical smoothing choices or parametric fits.

When using classical decompose(), how is the trend-cycle component typically estimated?

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