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Time Series Components
The investigation of many economic time series becomes problematic due to seasonal fluctuations. Series are made up of four components:
St: The Seasonal Component
Tt: The Trend Component
Ct: The Cyclical Component
It: The Error, or irregular component.
Unlike the trend and cyclical components, seasonal components, theoretically, happen with the same magnitude during the same time period each year. The seasonal component of a series are often considered uninteresting and cause a series to be ambiguous. By removing the seasonal component, it is easier to focus on other components.
Different statistical research groups have developed different methods of seasonal adjustment. The United States Census Bureau has developed X-12-ARIMA. The Federal Statistical Office of Germany has developed the application software BV4.1 for decomposing and seasonally adjustment which bases on the statistical method berlin procedure.
One famous example is the rate of unemployment which is also presented by a time series. Particularly this rate depends on seasonal influences. This is why it is important to free the unemployment rate of its seasonal component. As soon as the seasonal influence is removed from this time series the real trend of the unemployment rate is visible. Seasonal adjustment is mostly used in the official statistics implemented by statistical software.
When seasonal adjustment is not done with monthly data, year-on-year changes are utilised in a naive attempt to avoid contamination with seasonality. However, each year-on-year change is the sum of twelve monthly changes. This moving window (with a width of 12) is often a poor way to understand a series. As an example, Bhattacharya, Patnaik and Shah find that by using point-on-point changes of seasonally adjusted data, the analyst is able to better obtain early warnings in the inflation time-series.