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| Modello ARCH di Fourier× | Modello ARCH Non Lineare (NARCH)× | |
|---|---|---|
| Campo | Econometria | Econometria |
| Famiglia | Regression model | Regression model |
| Anno di origine≠ | 2010s | 1992 |
| Ideatore≠ | Extends Engle (1982) ARCH framework with Fourier terms following Enders & Lee (2012) | Higgins & Bera |
| Tipo≠ | Volatility model with smooth structural change | Volatility model |
| Fonte seminale≠ | Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50(4), 987–1007. DOI ↗ | Higgins, M. L., & Bera, A. K. (1992). A class of nonlinear ARCH models. International Economic Review, 33(1), 137-158. DOI ↗ |
| Alias | Fourier-ARCH, F-ARCH, ARCH with Fourier terms, Fourier smooth transition ARCH | NARCH, Nonlinear ARCH, nonlinear conditional heteroscedasticity model, NARCH model |
| Correlati≠ | 6 | 4 |
| Sintesi≠ | The Fourier ARCH model extends the classical ARCH framework by incorporating trigonometric (Fourier) terms into the conditional variance equation. This allows the model to capture smooth, gradual shifts in volatility dynamics over time without assuming abrupt structural breaks, making it well-suited for long financial or macroeconomic time series subject to slowly evolving regime changes. | The Nonlinear ARCH (NARCH) model, introduced by Higgins and Bera (1992), extends Engle's original ARCH framework by allowing the power transformation of volatility to be estimated from the data rather than fixed at two. This flexibility captures a broader class of volatility dynamics observed in financial and macroeconomic time series. |
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