Time series analysis and forecast, Extraction of seasonality components

Examples: Time series analysis

Extraction of seasonality components

The ‘Caterpillar’-SSA is a convenient technique for extraction of seasonality components and investigation of seasonality structure. Natural decomposition of the time series is constructed on the base of the unique parameter (the window length). Grouping paired harmonic components of the time series decomposition, you can extract seasonal component from the time series and to obtain its expansion into harmonics with varying amplitudes.

Figure 1.7: Sales of Fortified Wines: initial series and its trend

Figure 1.8: Sales of Fortified Wines: four leading seasonal harmonics

Data: "Wines", time series "Fort"
Description: sales of fortified wines in Australia (th. of liters), monthly, Jan 1980-Jun 1994
Source: Time Series Data Library maintained by Rob Hyndman
Parameters: window length = 84
Figure 1.7: the time series component reconstructed from the leading eigentriple (red line) and the initial time series
Figure 1.8: the time series components reconstructed from the eigentriples 2-3 (12-months harmonic), eigentriples 4-5 (4-months harmonic), eigentriples 6-7 (6-months harmonic), and eigentriples 8-9 (2.4-months harmonic)

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