مقایسهٔ روش‌ها

	مدل آریما فوریه	مدل خودرگرسیون میانگین متحرک غیرخطی (NARMA)
حوزه	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model
سال پیدایش	2004–2006	1980s–1990s
پدیدآور	Becker, Enders, and Hurn	Tong (1990); Granger & Terasvirta (1993)
نوع	Time series model with smooth structural change	Nonlinear time series model
منبع بنیادین	Becker, R., Enders, W., & Hurn, S. (2006). A general test for time dependence in parameters. Journal of Applied Econometrics, 21(7), 1005–1028.	Tong, H. (1990). Non-linear Time Series: A Dynamical System Approach. Oxford University Press. ISBN: 978-0198522300
نام‌های دیگر	Fourier ARMA, ARMA with Fourier terms, trigonometric ARMA, smooth structural change ARMA	NARMA, nonlinear ARMA, NLARMA, nonlinear autoregressive moving average
مرتبط	5	2
خلاصه	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.