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| ARIMA-modellen (Autoregressive Integrated Moving Average)× | Fourier ARIMA-modellen× | |
|---|---|---|
| Fagområde | Økonometri | Økonometri |
| Familie | Regression model | Regression model |
| Oprindelsesår≠ | 1970 | 2004-2012 |
| Ophavsperson≠ | George Box and Gwilym Jenkins | Becker, Enders, and Hurn; further extended by Enders and Lee |
| Type≠ | Time series forecasting model | Time series model |
| Oprindelig kilde≠ | Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day. link ↗ | Enders, W., & Lee, J. (2012). The flexible Fourier form and Dickey-Fuller type unit root tests. Economics Letters, 117(1), 196-202. DOI ↗ |
| Aliasser | ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q) | Fourier ARIMA, ARIMA with Fourier terms, trigonometric ARIMA, Fourier-flexible ARIMA |
| Relaterede≠ | 6 | 2 |
| Resumé≠ | The ARIMA(p,d,q) model is the standard workhorse for univariate time series forecasting. It combines autoregressive terms (past values), differencing to induce stationarity, and moving average terms (past shocks) into a unified linear framework. Developed by Box and Jenkins (1970), it remains one of the most widely applied models in econometrics and applied statistics. | 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. |
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