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. Typically, seasonally adjusted data is reported for unemployment rates to reveal the underlying trends and cycles in labor markets.
Time series components
The investigation of many economic time series becomes problematic due to seasonal fluctuations. Time series are made up of four components:
: The seasonal component
: The trend component
: The cyclical component
: 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.
The relation between decomposition of time series components
Additive decomposition: , where is the data at time . Multiplicative decomposition: . Logs turn multiplicative relationship into an additive relationship: : An additive model is appropriate if the magnitude of seasonal fluctuations does not vary with level. If seasonal fluctuations are proportional to the level of the series, then a multiplicative model is appropriate. Multiplicative decomposition is more prevalent with economic series.
Adjustment methods
Unlike the trend and cyclical components, seasonal components, theoretically, happen with similar magnitude during the same time period each year. The seasonal components of a series are sometimes considered to be uninteresting and to hinder the interpretation of a series. Removing the seasonal component directs focus on other components and will allow better analysis.
Different statistical research groups have developed different methods of seasonal adjustment, for example X-13-ARIMA and X-12-ARIMA developed by the United States Census Bureau; TRAMO/SEATS developed by the Bank of Spain; MoveReg (for weekly data) developed by the United States Bureau of Labor Statistics; STAMP developed by a group led by S. J. Koopman; and “Seasonal and Trend decomposition using Loess” (STL) developed by Cleveland et al. (1990). While X-12/13-ARIMA can only be applied to monthly or quarterly data, STL decomposition can be used on data with any type of seasonality. Furthermore, unlike X-12-ARIMA, STL allows the user to control the degree of smoothness of the trend cycle and how much the seasonal component changes over time. X-12-ARIMA can handle both additive and multiplicative decomposition whereas STL can only be used for additive decomposition. In order to achieve a multiplicative decomposition using STL, the user can take the log of the data before decomposing, and then back-transform after the decomposition.
Software
Each group provides software supporting their methods. Some versions are also included as parts of larger products, and some are commercially available. For example, SAS includes X-12-ARIMA, while Oxmetrics includes STAMP. A recent move by public organisations to harmonise seasonal adjustment practices has resulted in the development of Demetra+ by Eurostat and National Bank of Belgium which currently includes both X-12-ARIMA and TRAMO/SEATS. R includes STL decomposition. The X-12-ARIMA method can be utilized via the R package "X12". EViews supports X-12, X-13, Tramo/Seats, STL and MoveReg.
Example
One well-known example is the rate of unemployment, which is represented by a time series. This rate depends particularly on seasonal influences, which is why it is important to free the unemployment rate of its seasonal component. Such seasonal influences can be due to school graduates or dropouts looking to enter into the workforce and regular fluctuations during holiday periods. Once the seasonal influence is removed from this time series, the unemployment rate data can be meaningfully compared across different months and predictions for the future can be made.