Linganisha mbinu

	Mfumo wa Fourier AR	Modeli ya ARMA (Autoregressive Moving Average)
Nyanja	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model
Mwaka wa asili	2012	1970
Mwanzilishi	Enders & Lee	George E. P. Box and Gwilym M. Jenkins
Aina	Time series model with Fourier augmentation	Time series model
Chanzo asilia	Enders, W., & Lee, J. (2012). A unit root test using a Fourier series to approximate smooth breaks. Oxford Bulletin of Economics and Statistics, 74(4), 574–599.	Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day.
Majina mbadala	Fourier AR, trigonometric AR model, smooth transition AR with Fourier terms, FAR model	ARMA, Box-Jenkins model, autoregressive moving average, AR(p)MA(q)
Zinazohusiana	6	5
Muhtasari	The Fourier AR model extends the standard autoregressive specification by adding trigonometric (sine and cosine) terms to the deterministic component. This allows the model to capture smooth, gradual shifts in the mean or trend of a time series without requiring the researcher to locate or count structural break points explicitly.	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.