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| Fourier-ARIMA-Modell× | SARIMA-Modell× | |
|---|---|---|
| Fachgebiet | Ökonometrie | Ökonometrie |
| Familie | Regression model | Regression model |
| Entstehungsjahr≠ | 2004-2012 | 1970 (first edition); 1976 (revised) |
| Urheber≠ | Becker, Enders, and Hurn; further extended by Enders and Lee | Box, Jenkins, and Reinsel |
| Typ≠ | Time series model | Seasonal time series model |
| Wegweisende Quelle≠ | Enders, W., & Lee, J. (2012). The flexible Fourier form and Dickey-Fuller type unit root tests. Economics Letters, 117(1), 196-202. DOI ↗ | Box, G. E. P., Jenkins, G. M., & Reinsel, G. C. (1976). Time Series Analysis: Forecasting and Control (revised ed.). Holden-Day. ISBN: 978-0130607744 |
| Aliasnamen | Fourier ARIMA, ARIMA with Fourier terms, trigonometric ARIMA, Fourier-flexible ARIMA | SARIMA, seasonal ARIMA, Box-Jenkins seasonal model, ARIMA with seasonal component |
| Verwandt≠ | 2 | 5 |
| Zusammenfassung≠ | The Fourier ARIMA model augments a standard ARIMA specification with trigonometric sine and cosine terms, allowing it to capture smooth, gradual structural change and flexible nonlinear seasonality without specifying the exact timing or number of breaks in advance. It is widely used in applied macroeconometrics and finance for series exhibiting slowly evolving dynamics. | SARIMA extends ARIMA by adding seasonal autoregressive and moving-average operators to capture repeating patterns at fixed intervals — such as monthly, quarterly, or annual cycles. Denoted SARIMA(p,d,q)(P,D,Q)s, it is the standard workhorse for univariate seasonal time series forecasting in econometrics, economics, and official statistics. |
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