方法对比

	傅里叶移动平均 (Fourier MA) 模型	自回归积分滑动平均模型 (ARIMA)	傅里叶自回归积分滑动平均模型
领域	计量经济学	计量经济学	计量经济学
方法族	Regression model	Regression model	Regression model
起源年份	1990s–2000s	1970	2004-2012
提出者	Harvey, A. C.; Hyndman, R. J.	George Box and Gwilym Jenkins	Becker, Enders, and Hurn; further extended by Enders and Lee
类型	Time series model	Time series forecasting model	Time series model
开创性文献	Hyndman, R. J., & Athanasopoulos, G. (2021). Forecasting: Principles and Practice (3rd ed.). OTexts.	Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day.	Enders, W., & Lee, J. (2012). The flexible Fourier form and Dickey-Fuller type unit root tests. Economics Letters, 117(1), 196-202.
别名	Fourier MA, Fourier-augmented moving average, trigonometric MA model, harmonic moving average model	ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q)	Fourier ARIMA, ARIMA with Fourier terms, trigonometric ARIMA, Fourier-flexible ARIMA
相关	2	6	2
摘要	The Fourier MA model combines a Moving Average (MA) error structure with Fourier series terms — sine and cosine pairs — to capture complex or high-frequency seasonal patterns in time series data. It is particularly useful when the seasonal period is long or irregular, making classical seasonal ARIMA parameterisation infeasible.	The ARIMA(p,d,q) model is the standard workhorse for univariate time series forecasting. It combines autoregressive terms (past values), differencing to induce stationarity, and moving average terms (past shocks) into a unified linear framework. Developed by Box and Jenkins (1970), it remains one of the most widely applied models in econometrics and applied statistics.	The Fourier ARIMA model augments a standard ARIMA specification with trigonometric sine and cosine terms, allowing it to capture smooth, gradual structural change and flexible nonlinear seasonality without specifying the exact timing or number of breaks in advance. It is widely used in applied macroeconometrics and finance for series exhibiting slowly evolving dynamics.