Time series analysis and forecast, Extraction of cycles with small and large periods

Examples: Time series analysis

Extraction of cycles with small and large periods

The ‘Caterpillar’-SSA is an appropriate technique for simultaneous extraction of periodic components with different periods from the time series. Natural decomposition of the time series is automatically constructed on the base of the unique parameter (the window length). Grouping paired sinusoidal components of the decomposition, you can extract component with the periods; one period can be many times bigger than another one.

Figure 1.9: Births: initial time series and its annual periodicity

Figure 1.10: Births: one-week periodicity

Data: "Births"
Description: number of daily births, Quebec, Canada, from January 1, 1977 to December 31, 1990
Source: Time Series Data Library maintained by Rob Hyndman
Parameters: window length = 365
Figure 1.9: the time series component reconstructed from the eigentriples with numbers 1, 6-9, and 12-19 (red line) and the initial time series
Figure 1.10: first three months of the reconstruction from the eigentriples 2-5 and 10-11 (red line) and the initial time series

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