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Seasonal adjustment or deseasonalization is a statistical method for removing the seasonal component of a time series. It is usually done when wanting to analyse the trend, and cyclical deviations from trend, of a time series independently of the seasonal components. Many economic phenomena have seasonal cycles, such as agricultural production, (crop yields fluctuate with the seasons) and consumer consumption (increased personal spending leading up to Christmas). It is necessary to adjust for this component in order to understand underlying trends in the economy, so official statistics are often adjusted to remove seasonal components.[1] Typically, seasonally adjusted data is reported for unemployment rates to reveal the underlying trends and cycles in labor markets.[2][3]

## Time series components

The investigation of many economic time series becomes problematic due to seasonal fluctuations. Time series are made up of four components:

• ${\displaystyle S_{t}}$: The seasonal component
• ${\displaystyle T_{t}}$: The trend component
• ${\displaystyle C_{t}}$: The cyclical component
• ${\displaystyle E_{t}}$: The error, or irregular component.

The difference between seasonal and cyclic patterns:

• Seasonal patterns have a fixed and known length, while cyclic patterns have variable and unknown length.
• Cyclic pattern exists when data exhibit rises and falls that are not of fixed period (duration usually of at least 2 years).
• The average length of a cycle is usually longer than that of seasonality.
• The magnitude of cyclic variation is usually more variable than that of seasonal variation.[4]

The relation between decomposition of time series components

• Additive decomposition: ${\displaystyle Y_{t}=S_{t}+T_{t}+C_{t}+E_{t}}$, where