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| Model ARMA Fouriera× | Model nieliniowy ARMA (NARMA)× | |
|---|---|---|
| Dziedzina | Ekonometria | Ekonometria |
| Rodzina | Regression model | Regression model |
| Rok powstania≠ | 2004–2006 | 1980s–1990s |
| Twórca≠ | Becker, Enders, and Hurn | Tong (1990); Granger & Terasvirta (1993) |
| Typ≠ | Time series model with smooth structural change | Nonlinear time series model |
| Źródło pierwotne≠ | Becker, R., Enders, W., & Hurn, S. (2006). A general test for time dependence in parameters. Journal of Applied Econometrics, 21(7), 1005–1028. link ↗ | Tong, H. (1990). Non-linear Time Series: A Dynamical System Approach. Oxford University Press. ISBN: 978-0198522300 |
| Inne nazwy | Fourier ARMA, ARMA with Fourier terms, trigonometric ARMA, smooth structural change ARMA | NARMA, nonlinear ARMA, NLARMA, nonlinear autoregressive moving average |
| Pokrewne≠ | 5 | 2 |
| Podsumowanie≠ | 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 Nonlinear ARMA (NARMA) model extends the classical linear ARMA framework by allowing the conditional mean to depend on past observations and past errors through an arbitrary nonlinear function. It captures complex dynamics — such as regime changes, asymmetric cycles, and threshold effects — that linear models miss, making it valuable for economic and financial time series. |
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