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Unobserved components model

Seasonality Thomas Url Österreichisches Institut für Wirtschaftsforschung (WIFO) Wirtschaftsuniversität Wien. Unobserved components model. Multiplicative model. Additive model. p t : Trend component c t : Cyclical component s t : Seasonal component  t : Irregular component.

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Unobserved components model

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  1. SeasonalityThomas UrlÖsterreichisches Institut für Wirtschaftsforschung (WIFO)Wirtschaftsuniversität Wien

  2. Unobservedcomponents model Multiplicative model Additive model • pt: Trend component • ct: Cyclicalcomponent • st: Seasonalcomponent • t: Irregularcomponent Fußzeile

  3. A simple deterministic model with Fußzeile

  4. A trigonometricseasonal Fußzeile

  5. A trigonometricseasonal Fußzeile

  6. Movingaverage • Reproduces movingfeaturesofseasonality • Chooseweightstocapturevariation • Ad hoc filter • Start- and end-pointproblems Fußzeile

  7. X11 and X12 Filter • (1) Detrend x(t) bysubstracting a 2x12 MA • (1) Take initialseasonalandapply MA (3x3) togetpreliminaryseasonalcomponent • (1) Subtract 2x12 MA frompreliminaryseasonal • (1) Subtractresultfrom x(t) togetpreliminaryseasonaladjustedseries • (2) Subtract Henderson trend MA ofthisfrom x(t) togetrefineddetrended • (2) Apply (3x5) seasonal MA toresultfrombeforeandsubtract 2x12 MA toget final seasonalcomponent • (3) Compute final trendandirregularcomponents Fußzeile

  8. X11 and X12 Filter Example 3x3 MA: Final Trend and irreg.: Fußzeile

  9. X11 and X12 Filter Fußzeile

  10. Spectrumof a process Fußzeile

  11. X11 gainfunction Fußzeile

  12. Outliers Fußzeile

  13. Spectral AMB decomposition Fußzeile

  14. Frequencydomain AMB decomposition Fußzeile

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