Time series analysis and forecast, Complex trends and periodicities

Examples: Time series analysis

Complex trends and periodicities

The ‘Caterpillar’-SSA technique allows to extract simultaneously both the complex trend and the periodics with the complex structure (varying amplitudes). Natural decomposition of the time series is constructed on the base of the unique parameter (the window length). Grouping smooth low-frequency components of the decomposition together and oscillation components together, you can extract both the trend and the amplitude-modulated seasonality.

Figure 1.12: Unemployment: trend

Figure 1.13: Unemployment: seasonality

Data: "Unemployment"
Description: West Germany, monthly, from April 1950 to December 1980
Source: Time Series Data Library maintained by Rob Hyndman
Parameters: window length = 180
Figure 1.12: the time series component reconstructed from the eigentriples with numbers 1, 2, 5-7, 10, 11, 14, 15, 20, 21, 24, 27, 30, and 33 (red line) and the initial time series
Figure 1.13: the time series component reconstructed from the eigentriples 3, 4, 8, 9, 12, 13, 16-19, 22, 23, 25, 26, 34, 35, 43, 44, 71, and 72

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