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| Modello ARMA di Fourier× | Modello ARMA (Autoregressive Moving Average)× | |
|---|---|---|
| Campo | Econometria | Econometria |
| Famiglia | Regression model | Regression model |
| Anno di origine≠ | 2004–2006 | 1970 |
| Ideatore≠ | Becker, Enders, and Hurn | George E. P. Box and Gwilym M. Jenkins |
| Tipo≠ | Time series model with smooth structural change | Time series model |
| Fonte seminale≠ | Becker, R., Enders, W., & Hurn, S. (2006). A general test for time dependence in parameters. Journal of Applied Econometrics, 21(7), 1005–1028. link ↗ | Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day. link ↗ |
| Alias | Fourier ARMA, ARMA with Fourier terms, trigonometric ARMA, smooth structural change ARMA | ARMA, Box-Jenkins model, autoregressive moving average, AR(p)MA(q) |
| Correlati | 5 | 5 |
| Sintesi≠ | The Fourier ARMA model augments the classical Autoregressive Moving Average framework with low-frequency Fourier (sine and cosine) terms to capture smooth, gradual shifts in the mean or trend of a time series. Unlike dummy-variable approaches, it requires no prior knowledge of when structural change occurred, approximating change with flexible trigonometric functions. | The ARMA(p,q) model describes a stationary time series as a combination of two components: an autoregressive part that regresses the current value on its own past p values, and a moving average part that accounts for past q error terms. It is the foundational framework of the Box-Jenkins methodology for univariate time series modelling and short-run forecasting. |
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