Seasonality Thomas Url Österreichisches Institut für Wirtschaftsforschung (WIFO) Wirtschaftsuniversität Wien

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  • Slide 1
  • Seasonality Thomas Url sterreichisches Institut fr Wirtschaftsforschung (WIFO) Wirtschaftsuniversitt Wien
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  • Unobserved components model FUZEILESEITE 2 p t : Trend component c t : Cyclical component s t : Seasonal component t : Irregular component Multiplicative model Additive model
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  • A simple deterministic model FUZEILESEITE 3 with
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  • A trigonometric seasonal FUZEILESEITE 4
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  • A trigonometric seasonal FUZEILESEITE 5
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  • Moving average FUZEILESEITE 6 Reproduces moving features of seasonality Choose weights to capture variation Ad hoc filter Start- and end-point problems
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  • X11 and X12 Filter FUZEILESEITE 7 (1) Detrend x(t) by substracting a 2x12 MA (1) Take initial seasonal and apply MA (3x3) to get preliminary seasonal component (1) Subtract 2x12 MA from preliminary seasonal (1) Subtract result from x(t) to get preliminary seasonal adjusted series (2) Subtract Henderson trend MA of this from x(t) to get refined detrended (2) Apply (3x5) seasonal MA to result from before and subtract 2x12 MA to get final seasonal component (3) Compute final trend and irregular components
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  • X11 and X12 Filter FUZEILESEITE 8 Example 3x3 MA: Final Trend and irreg.:
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  • X11 and X12 Filter FUZEILESEITE 9
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  • Spectrum of a process FUZEILESEITE 10
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  • X11 gain function FUZEILESEITE 11
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  • Outliers FUZEILESEITE 12
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  • Spectral AMB decomposition FUZEILESEITE 13
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  • Frequency domain AMB decomposition FUZEILESEITE 14