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| Modello Autoregressivo Non Lineare (NAR)× | Modello ARMA (Autoregressive Moving Average)× | Modello Autoregressivo (AR)× | |
|---|---|---|---|
| Campo | Econometria | Econometria | Econometria |
| Famiglia | Regression model | Regression model | Regression model |
| Anno di origine≠ | 1978-1990 | 1970 | 1970s (popularised 1976) |
| Ideatore≠ | Tong, H. (threshold AR); Terasvirta, T. (STAR variant) | George E. P. Box and Gwilym M. Jenkins | George E. P. Box and Gwilym M. Jenkins |
| Tipo≠ | Nonlinear time series model | Time series model | Time series model |
| Fonte seminale≠ | Tong, H. (1990). Non-Linear Time Series: A Dynamical System Approach. Oxford University Press. ISBN: 9780198522201 | Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day. link ↗ | Box, G. E. P., & Jenkins, G. M. (1976). Time Series Analysis: Forecasting and Control (revised ed.). Holden-Day. ISBN: 978-0816211043 |
| Alias | NAR model, nonlinear autoregression, NLAR, threshold autoregressive model | ARMA, Box-Jenkins model, autoregressive moving average, AR(p)MA(q) | AR model, AR(p) model, autoregression, AR process |
| Correlati≠ | 6 | 5 | 6 |
| Sintesi≠ | The Nonlinear AR model extends the classical autoregressive framework by allowing the mapping from past values to the current value to follow an arbitrary or regime-switching nonlinear function. Major families include the Self-Exciting Threshold AR (SETAR), Smooth Transition AR (STAR), and neural network AR, each capturing different forms of asymmetry, regime shifts, or smooth nonlinear dynamics in univariate time series. | 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. | An autoregressive model of order p — AR(p) — expresses the current value of a time series as a linear function of its own p most recent past values plus a white-noise error. It is the building block of the Box-Jenkins family of time-series models and is widely used for forecasting stationary economic and financial series. |
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